P. Thomas, P. Genton, E. Paris, P. Chauvel, P. Buser et al., The "epileptogenic zone" in humans: representation of intercritical events by spatiotemporal maps [3] P. ChauvelIndications et méthodes du traitement chirurgical des épilepsiesAn analysis of clinical seizure patterns and their localizing value in frontal and temporal lobe epilepsiesExtraction of epileptic signatures and coherence estimation in SEEG observations: a preliminary study, Rev Neurol Brain Innov. Techn. Biol. Med, vol.143, issue.197, pp.443-50, 1987.

E. Wyllie, The treatment of epilepsy : principles and practiceProposal for revised clinical and electroencephalographic classification of epileptic seizures. From the Commission on Classification and Terminology of the International League Against Epilepsy, Penfield and H. H. Jasper, Epilepsy and the functional anatomy of the human brain, pp.489-501, 1954.

I. A. Awad, J. Rosenfeld, J. Ahl, J. F. Hahn, and H. Luders, Intractable Epilepsy and Structural Lesions of the Brain: Mapping, Resection Strategies, and Seizure Outcome, Epilepsia, vol.37, issue.2, pp.179-86, 1991.
DOI : 10.1016/0006-8993(72)90403-9

J. Bourien, Analyse de distributions spatio-temporelles de transitoires dans des signaux vectoriels. Application à la détection-classification d'activités paroxystiques intercritiques dans des observations EEG, Rennes: Université de Rennes, vol.1, 2003.
URL : https://hal.archives-ouvertes.fr/tel-00007178

B. Gourévitch, Etude des mécanismes corticaux auditifs par l'analyse de l'enveloppe temporelle, Rennes: Université de Rennes, vol.1, 2005.

J. Talairach and J. Bancaud, Stereotaxic exploration and therapy in epilepsy, The Epilepsies, pp.758-782, 1974.

J. Talairach, J. Bancaud, G. Szikla, A. Bonis, S. Geier et al., New approach to the neurosurgery of epilepsy Stereotaxic methodology and therapeutic results. 1. Introduction and history, Neurochirurgie, vol.20, pp.1-240, 1974.

L. Senhadji, A. Hernandez, F. Wendling, and G. Carrault, Sur les signaux électrophysiologiques : réflexion et quelques perspectives ouvertes, GRETSI, pp.241-244, 2005.

T. I. Netoff and S. J. Schiff, Decreased neuronal synchronization during experimental seizures, J Neurosci, vol.22, pp.7297-307, 2002.

F. Wendling, F. Bartolomei, J. J. Bellanger, J. Bourien, and P. Chauvel, Epileptic fast intracerebral EEG activity: evidence for spatial decorrelation at seizure onset, Brain, vol.126, issue.6, pp.1449-1459, 2003.
DOI : 10.1093/brain/awg144

URL : https://hal.archives-ouvertes.fr/inserm-00149231

F. Mormann, T. Kreuz, C. Rieke, R. G. Andrzejak, A. Kraskov et al., On the predictability of epileptic seizures, Clinical Neurophysiology, vol.116, issue.3, pp.569-587, 2005.
DOI : 10.1016/j.clinph.2004.08.025

J. S. Barlow and M. A. Brazier, A note on a correlator for electroencephalographic work, Electroencephalography and Clinical Neurophysiology, vol.6, pp.321-326, 1954.
DOI : 10.1016/0013-4694(54)90036-X

M. A. Brazier, Studies of the EEG activity of limbic structures in man, Electroencephalography and Clinical Neurophysiology, vol.25, issue.4, pp.309-327, 1968.
DOI : 10.1016/0013-4694(68)90171-5

G. Pfurtscheller and C. Andrew, Event-Related Changes of Band Power and Coherence: Methodology and Interpretation, Journal of Clinical Neurophysiology, vol.16, issue.6, pp.512-519, 1999.
DOI : 10.1097/00004691-199911000-00003

P. J. Franaszczuk and G. K. Bergey, An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals, Biological Cybernetics, vol.81, issue.1, pp.3-9, 1999.
DOI : 10.1007/s004220050540

S. Haykin, R. J. Racine, Y. Xu, and C. A. Chapman, Monitoring neuronal oscillations and signal transmission between cortical regions using time-frequency analysis of electroencephalographic activity, Proceedings of the IEEE, vol.84, issue.9, pp.1295-1301, 1996.
DOI : 10.1109/5.535247

N. J. Mars and F. H. Lopes-da-silva, Propagation of seizure activity in kindled dogs, Electroencephalography and Clinical Neurophysiology, vol.56, issue.2, pp.194-209, 1983.
DOI : 10.1016/0013-4694(83)90074-3

J. P. Pijn and F. H. Lopes-da-silva, Propagation of Electrical Activity: Nonlinear Associations and Time Delays between EEG Signals, Basic Mechanisms of the Eeg, pp.41-61, 1993.
DOI : 10.1007/978-1-4612-0341-4_4

F. Wendling, F. Bartolomei, J. J. Bellanger, and P. Chauvel, Interpretation of interdependencies in epileptic signals using a macroscopic physiological model of the EEG, Clinical Neurophysiology, vol.112, issue.7, pp.1201-1218, 2001.
DOI : 10.1016/S1388-2457(01)00547-8

L. D. Iasemidis, Epileptic seizure prediction and control, IEEE Transactions on Biomedical Engineering, vol.50, issue.5, pp.549-58, 2003.
DOI : 10.1109/TBME.2003.810705

K. Lehnertz, Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy ??? an overview, International Journal of Psychophysiology, vol.34, issue.1, pp.45-52, 1999.
DOI : 10.1016/S0167-8760(99)00043-4

R. Q. Quiroga, A. Kraskov, T. Kreuz, and P. Grassberger, Reply to ???Comment on ???Performance of different synchronization measures in real data: A case study on electroencephalographic signals??? ???, Physical Review E, vol.72, issue.6, p.41903, 2002.
DOI : 10.1103/PhysRevE.72.063902

O. David, D. Cosmelli, and K. J. Friston, Evaluation of different measures of functional connectivity using a neural mass model, NeuroImage, vol.21, issue.2, pp.659-673, 2004.
DOI : 10.1016/j.neuroimage.2003.10.006

E. Pereda, D. M. Delacruz, L. Devera, and J. J. Gonzalez, Comparing Generalized and Phase Synchronization in Cardiovascular and Cardiorespiratory Signals, IEEE Transactions on Biomedical Engineering, vol.52, issue.4, pp.578-583, 2005.
DOI : 10.1109/TBME.2005.844022

M. A. Brazier and J. S. Barlow, Some applications of correlation analysis to clinical problems in electroencephalography, Electroencephalography and Clinical Neurophysiology, vol.8, issue.2, pp.325-356, 1956.
DOI : 10.1016/0013-4694(56)90124-9

W. R. Adey, D. O. Walter, and C. E. Hendrix, Computer techniques in correlation and spectral analyses of cerebral slow waves during discriminative behavior, Experimental Neurology, vol.3, issue.6, pp.501-524, 1961.
DOI : 10.1016/S0014-4886(61)80002-2

C. M. Clark, R. Kessler, M. S. Buchsbaum, R. A. Margolin, and H. H. Holcomb, Correlational methods for determining regional coupling of cerebral glucose metabolism: a pilot study, Biological Psychiatry, vol.19, pp.663-678, 1984.

B. Horwitz, R. Duara, and S. I. Rapoport, Intercorrelations of Glucose Metabolic Rates between Brain Regions: Application to Healthy Males in a State of Reduced Sensory Input, Journal of Cerebral Blood Flow & Metabolism, vol.19, issue.4, pp.484-499, 1984.
DOI : 10.1111/j.1471-4159.1977.tb10649.x

J. C. Shaw, Correlation and coherence analysis of the EEG: A selective tutorial review, International Journal of Psychophysiology, vol.1, issue.3, pp.255-266, 1984.
DOI : 10.1016/0167-8760(84)90045-X

A. S. Gevins, J. C. Doyle, and B. A. Cutillo, Neurocognitive Pattern Analysis of a Visuospatial Task: Rapidly-Shifting Foci of Evoked Correlations Between Electrodes, Psychophysiology, vol.68, issue.1, pp.32-43, 1985.
DOI : 10.1016/0013-4694(51)90074-0

E. J. Bartlett, J. W. Brown, A. P. Wolf, and J. D. Brodie, Correlations between glucose metabolic rates in brain regions of healthy male adults at rest and during language stimulation*1, Brain and Language, vol.32, issue.1, pp.1-18, 1987.
DOI : 10.1016/0093-934X(87)90115-5

J. Lachaux, M. Chavez, and A. Lutz, A simple measure of correlation across time, frequency and space between continuous brain signals, Journal of Neuroscience Methods, vol.123, issue.2, pp.175-188, 2003.
DOI : 10.1016/S0165-0270(02)00358-8

E. W. Weisstein, CRC concise encyclopedia of mathematics, 2003.

G. M. Jenkins and D. G. Watts, Spectral analysis and its applications, 1968.

L. H. Koopmans, The spectral analysis of time series, 1995.

J. S. Bendat and A. G. Piersol, Engineering applications of correlation and spectral analysis, 1993.

J. S. Bendat and A. G. Piersol, Random data : analysis and measurement procedures, 2000.
DOI : 10.1002/9781118032428

G. Carter, C. Knapp, and A. Nuttall, Estimation of the magnitude-squared coherence function via overlapped fast Fourier transform processing, IEEE Transactions on Audio and Electroacoustics, vol.21, issue.4, pp.337-344, 1973.
DOI : 10.1109/TAU.1973.1162496

G. C. Carter, Coherence and time delay estimation, Proceedings of the IEEE, vol.75, issue.2, pp.236-255, 1987.
DOI : 10.1109/PROC.1987.13723

W. A. Gardner, A unifying view of coherence in signal processing, Signal Processing, vol.29, issue.2, pp.113-140, 1992.
DOI : 10.1016/0165-1684(92)90015-O

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

D. O. Walter and W. R. Adey, Analysis of Brain-Wave Generators as Multiple Statistical Time Series, IEEE Transactions on Biomedical Engineering, vol.12, issue.1, pp.8-13, 1965.
DOI : 10.1109/TBME.1965.4502335

M. A. Brazier, Spread of seizure discharges in epilepsy: Anatomical and electrophysiological considerations, Experimental Neurology, vol.36, issue.2, pp.263-72, 1972.
DOI : 10.1016/0014-4886(72)90022-2

F. Bartolomei, F. Wendling, J. Vignal, S. Kochen, J. Bellanger et al., Seizures of temporal lobe epilepsy: identification of subtypes by coherence analysis using stereo-electro-encephalography, Clinical Neurophysiology, vol.110, issue.10, pp.1741-1754, 1999.
DOI : 10.1016/S1388-2457(99)00107-8

F. Wendling, F. Bartolomei, J. J. Bellanger, and P. Chauvel, Interpretation of interdependencies in epileptic signals using a macroscopic physiological model of the EEG, Clinical Neurophysiology, vol.112, issue.7, pp.1201-1219, 2001.
DOI : 10.1016/S1388-2457(01)00547-8

B. J. Winer, D. R. Brown, and K. M. Michels, Statistical principles in experimental design, 1991.
DOI : 10.1037/11774-000

J. Fox, Multiple and generalized nonparametric regression, 2000.
DOI : 10.4135/9781412985154

J. Fox, Nonparametric simple regression : smoothing scatterplots, 2000.
DOI : 10.4135/9781412985307

T. Hastie and R. Tibshirani, Generalized additive models, 1990.

J. P. Pijn, Quantitative evaluation of EEG signals in epilepsy, nonlinear associations, time delays and nonlinear dynamics Amsterdam: University of Amsterdam, 1990.

F. Lopes-da-silva, J. P. Pijn, and P. Boeijinga, Interdependence of EEG signals: Linear vs. nonlinear Associations and the significance of time delays and phase shifts, Brain Topography, vol.17, issue.1-2, pp.9-18, 1989.
DOI : 10.1007/BF01128839

M. Chavez, M. L. Van-quyen, V. Navarro, M. Baulac, and J. Martinerie, Spatio-temporal dynamics prior to neocortical seizures: amplitude versus phase couplings, IEEE Transactions on Biomedical Engineering, vol.50, issue.5, pp.571-583, 2003.
DOI : 10.1109/TBME.2003.810696

F. Wendling, F. Bartolomei, J. J. Bellanger, and P. Chauvel, Identification de r??seaux ??pileptog??nes par mod??lisation et analyse non lin??aire des signaux SEEG, Neurophysiologie Clinique/Clinical Neurophysiology, vol.31, issue.3, pp.139-151, 2001.
DOI : 10.1016/S0987-7053(01)00255-6

D. N. Velis, G. J. Brekelmans, J. P. Pijn, J. De-vries, W. Van-emde et al., Use of nonlinear association-and-delay analysis offers advantages in interpreting generalized epileptiform discharges, Electroencephalography and Clinical Neurophysiology, vol.103, issue.1, p.174, 1997.
DOI : 10.1016/S0013-4694(97)88819-4

V. M. Fernandes-de-lima, J. P. Pijn, C. N. Filipe, F. Lopes, and . Silva, The role of hippocampal commissures in the interhemispheric transfer of epileptiform afterdischarges in the rat: a study using linear and non-linear regression analysis, Electroencephalography and Clinical Neurophysiology, vol.76, issue.6, pp.520-539, 1990.
DOI : 10.1016/0013-4694(90)90003-3

C. E. Shannon and W. Weaver, The mathematical theory of communication, 1949.

R. M. Gray, Entropy and information theory, 1990.

T. M. Cover and J. A. Thomas, Elements of information theory, 1991.

G. A. Darbellay and I. Vajda, Estimation of the information by an adaptive partitioning of the observation space Information Theory, IEEE Transactions on, vol.45, pp.1315-1321, 1999.

A. M. Fraser and H. L. Swinney, Independent coordinates for strange attractors from mutual information, Physical Review A, vol.33, issue.2, pp.1134-1140, 1986.
DOI : 10.1103/PhysRevA.33.1134

P. Grassberger, Finite sample corrections to entropy and dimension estimates, Physics Letters A, vol.128, issue.6-7, pp.369-373, 1988.
DOI : 10.1016/0375-9601(88)90193-4

K. Pawelzik and H. G. Schuster, Generalized dimensions and entropies from a measured time series, Physical Review A, vol.35, issue.1, pp.481-485, 1987.
DOI : 10.1103/PhysRevA.35.481

T. Schreiber, Measuring Information Transfer, Physical Review Letters, vol.85, issue.2, 2000.
DOI : 10.1103/PhysRevLett.85.461

M. Palus, V. Komarek, Z. Hrncir, and K. Sterbova, Synchronization as adjustment of information rates: Detection from bivariate time series, Physical Review E, vol.63, issue.4, p.46211, 2001.
DOI : 10.1103/PhysRevE.63.046211

P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky et al., Phase Locking from Noisy Data: Application to Magnetoencephalography, Physical Review Letters, vol.81, issue.15, pp.3291-3294, 1998.
DOI : 10.1103/PhysRevLett.81.3291

A. G. Rossberg, K. Bartholomé, and J. Timmer, Data-driven optimal filtering for phase and frequency of noisy oscillations: Application to vortex flow metering, Physical Review E, vol.69, issue.1, 2004.
DOI : 10.1103/PhysRevE.69.016216

A. S. Pikovsky, M. G. Rosenblum, G. V. Osipov, and J. Kurths, Phase synchronization of chaotic oscillators by external driving, Physica D: Nonlinear Phenomena, vol.104, issue.3-4, pp.219-238, 1997.
DOI : 10.1016/S0167-2789(96)00301-6

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phase Synchronization of Chaotic Oscillators, Physical Review Letters, vol.76, issue.11, pp.1804-1807, 1996.
DOI : 10.1103/PhysRevLett.76.1804

P. Ashwin, Nonlinear dynamics: Synchronization from chaos, Nature, vol.422, issue.6930, pp.384-385, 2003.
DOI : 10.1016/0375-9601(92)90745-8

F. N. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. , Generalized synchronization of chaos in directionally coupled chaotic systems, Physical Review E, vol.51, issue.2, 1995.
DOI : 10.1103/PhysRevE.51.980

M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Identification of coupling direction: Application to cardiorespiratory interaction, Physical Review E, vol.65, issue.4, 2002.
DOI : 10.1103/PhysRevE.65.041909

M. G. Rosenblum and A. S. Pikovsky, Detecting direction of coupling in interacting oscillators, Physical Review E, vol.64, issue.4, 2001.
DOI : 10.1103/PhysRevE.64.045202

J. Bhattacharya, Reduced degree of long-range phase synchrony in pathological human brain, Acta Neurobiol. Exp, vol.61, pp.309-318, 2001.

W. Freeman, B. C. Bruke, and M. D. Holmes, Aperiodic phase re-setting in scalp EEG of beta-gamma oscillations by state transitions at alpha-theta rates, Human Brain Mapping, vol.394, issue.4, pp.248-272, 2003.
DOI : 10.1002/hbm.10120

A. Stefanovska, H. Haken, P. V. Mcclintock, M. Hozic, F. Bajrovic et al., Reversible Transitions between Synchronization States of the Cardiorespiratory System, Physical Review Letters, vol.85, issue.22, 2000.
DOI : 10.1103/PhysRevLett.85.4831

B. Blasius and L. Stone, CHAOS AND PHASE SYNCHRONIZATION IN ECOLOGICAL SYSTEMS, International Journal of Bifurcation and Chaos, vol.10, issue.10, pp.2361-2380, 2000.
DOI : 10.1142/S0218127400001511

J. Bhattacharya, E. Pereda, R. Kariyappa, and P. P. , Application of Nonlinear Analysis to Intensity Oscillations of the Chromospheric Bright Points, Solar Physics, vol.199, issue.2, pp.267-290, 2001.
DOI : 10.1023/A:1010370119746

D. J. Deshazer, R. Breban, E. Ott, and R. R. , Detecting Phase Synchronization in a Chaotic Laser Array, Physical Review Letters, vol.87, issue.4, 2001.
DOI : 10.1103/PhysRevLett.87.044101

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, The synchronization of chaotic systems, Physics Reports, vol.366, issue.1-2, pp.1-101, 2002.
DOI : 10.1016/S0370-1573(02)00137-0

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization : a universal concept in nonlinear sciences, 2001.
DOI : 10.1017/CBO9780511755743

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, pp.429-457, 1946.
DOI : 10.1049/ji-1.1947.0015

J. Lachaux, E. Rodriguez, M. L. Van-quyen, A. Lutz, J. Martinerie et al., STUDYING SINGLE-TRIALS OF PHASE SYNCHRONOUS ACTIVITY IN THE BRAIN, International Journal of Bifurcation and Chaos, vol.10, issue.10, pp.2429-2439, 2000.
DOI : 10.1142/S0218127400001560

J. Lachaux, E. Rodriguez, J. Martinerie, and F. J. Varela, Measuring phase synchrony in brain signals, Human Brain Mapping, vol.28, issue.4, pp.194-208, 1999.
DOI : 10.1002/(SICI)1097-0193(1999)8:4<194::AID-HBM4>3.0.CO;2-C

P. F. Panter, Modulation, noise, and spectral analysis, applied to information transmission, 1965.

A. Reilly, G. Frazer, and B. Boashash, Analytic signal generation-tips and traps, Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, pp.3241-3245, 1994.
DOI : 10.1109/78.330385

URL : http://espace.library.uq.edu.au/collection/UQ:183940

L. Marple and J. , Computing the discrete-time analytic signal via FFT, Signal Processing IEEE Transactions on [see also Acoustics, Speech, and Signal Processing IEEE Transactions on], vol.47, pp.2600-2603, 1999.

L. Senhadji, Approche multiresolution pour l'analyse des signaux non-stationnaires, Rennes, 1993.

M. L. Van-quyen, J. Foucher, J. Lachaux, E. Rodriguez, A. Lutz et al., Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony, Journal of Neuroscience Methods, vol.111, issue.2, pp.83-98, 2001.
DOI : 10.1016/S0165-0270(01)00372-7

F. Mormann, K. Lehnertz, P. David, and C. E. Elger, Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients, Physica D: Nonlinear Phenomena, vol.144, issue.3-4, pp.358-369, 2000.
DOI : 10.1016/S0167-2789(00)00087-7

R. K. Otnes and L. D. Enochson, Digital Time Series Analysis, Journal of Dynamic Systems, Measurement, and Control, vol.95, issue.4, 1972.
DOI : 10.1115/1.3426753

M. Rosenblum, A. Pikovsky, and J. Kurths, SYNCHRONIZATION APPROACH TO ANALYSIS OF BIOLOGICAL SYSTEMS, Fluctuation and Noise Letters, vol.04, issue.01, pp.53-62, 2004.
DOI : 10.1142/S0219477504001653

H. Fujisaka and T. Yamada, Stability Theory of Synchronized Motion in Coupled-Oscillator Systems, Progress of Theoretical Physics, vol.69, issue.1, pp.32-47, 1983.
DOI : 10.1143/PTP.69.32

V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Stochastic synchronization of oscillation in dissipative systems, Radiophysics and Quantum Electronics, vol.89, issue.No. 10, p.795, 1986.
DOI : 10.1007/BF01034476

T. L. Carroll and L. M. Pecora, Cascading synchronized chaotic systems, Physica D: Nonlinear Phenomena, vol.67, issue.1-3, pp.126-140, 1993.
DOI : 10.1016/0167-2789(93)90201-B

A. E. Hramov and A. A. Koronovskii, Generalized synchronization: A modified system approach, Physical Review E, vol.71, issue.6, pp.67201-67205, 2005.
DOI : 10.1103/PhysRevE.71.067201

K. Pyragas, Weak and strong synchronization of chaos, Phys. Rev. E, vol.54, 1996.

H. D. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Generalized synchronization of chaos: The auxiliary system approach, Physical Review E, vol.53, issue.5, pp.4528-4535, 1996.
DOI : 10.1103/PhysRevE.53.4528

L. M. Pecora, T. L. Carroll, and J. F. Heagy, Statistics for mathematical properties of maps between time series embeddings, Physical Review E, vol.52, issue.4, p.3420, 1995.
DOI : 10.1103/PhysRevE.52.3420

L. M. Pecora and T. L. Carroll, Driving systems with chaotic signals, Physical Review A, vol.44, issue.4, 1991.
DOI : 10.1103/PhysRevA.44.2374

F. Takens, Detecting strange attractors in turbulence, Lecture Nontes in Mathematics, vol.20, issue.1, p.366, 1981.
DOI : 10.1007/BF01646553

T. Sauer, J. A. Yorke, and M. Casdagli, Embedology, Journal of Statistical Physics, vol.22, issue.3-4, pp.579-616, 1991.
DOI : 10.1007/BF01053745

A. M. Albano, J. Muench, C. Schwartz, A. I. Mees, and P. E. Rapp, Singular-value decomposition and the Grassberger-Procaccia algorithm, Physical Review A, vol.38, issue.6, pp.3017-3026, 1988.
DOI : 10.1103/PhysRevA.38.3017

A. M. Fraser, Information and entropy in strange attractors Information Theory, IEEE Transactions on, vol.35, pp.245-262, 1989.

H. D. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, The analysis of observed chaotic data in physical systems, Reviews of Modern Physics, vol.65, issue.4, pp.1331-1392, 1993.
DOI : 10.1103/RevModPhys.65.1331

E. Ott, T. Sauer, and J. A. Yorke, Coping with chaos : analysis of chaotic data and the exploitation of chaotic systems, 1994.

P. Grassberger and I. Procaccia, Characterization of Strange Attractors, Physical Review Letters, vol.50, issue.5, pp.346-349, 1983.
DOI : 10.1103/PhysRevLett.50.346

D. S. Broomhead and G. P. King, Extracting qualitative dynamics from experimental data, Physica D: Nonlinear Phenomena, vol.20, issue.2-3, pp.217-236, 1986.
DOI : 10.1016/0167-2789(86)90031-X

A. I. Mees, P. E. Rapp, and L. S. Jennings, Singular-value decomposition and embedding dimension, Physical Review A, vol.36, issue.1, pp.340-346, 1987.
DOI : 10.1103/PhysRevA.36.340

M. B. Kennel, R. Brown, and H. D. , Determining embedding dimension for phase-space reconstruction using a geometrical construction, Plasmas, Fluids, and Related Interdisciplinary Topics), pp.3403-3411, 1992.
DOI : 10.1103/PhysRevA.45.3403

L. Cao, Practical method for determining the minimum embedding dimension of a scalar time series, Physica D: Nonlinear Phenomena, vol.110, issue.1-2, pp.43-50, 1997.
DOI : 10.1016/S0167-2789(97)00118-8

H. B. Fotsin and J. Daafouz, Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification, Physics Letters A, vol.339, issue.3-5, pp.304-315, 2005.
DOI : 10.1016/j.physleta.2005.03.049

J. Arnhold, P. Grassberger, K. Lehnertz, and C. E. Elger, A robust method for detecting interdependences: application to intracranially recorded EEG, Physica D: Nonlinear Phenomena, vol.134, issue.4, pp.419-430, 1999.
DOI : 10.1016/S0167-2789(99)00140-2

S. J. Schiff, P. So, T. Chang, R. E. Burke, and T. Sauer, Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble, Physical Review E, vol.54, issue.6, pp.6708-6724, 1996.
DOI : 10.1103/PhysRevE.54.6708

M. L. Van-quyen, C. Adam, M. Baulac, J. Martinerie, and F. J. Varela, Nonlinear interdependencies of EEG signals in human intracranially recorded temporal lobe seizures, Brain Research, vol.792, issue.1, pp.24-40, 1998.
DOI : 10.1016/S0006-8993(98)00102-4

M. L. Van-quyen, J. Martinerie, C. Adam, and F. J. Varela, Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy, Physica D: Nonlinear Phenomena, vol.127, issue.3-4, pp.250-266, 1999.
DOI : 10.1016/S0167-2789(98)00258-9

R. Quian-quiroga, J. Arnhold, and P. Grassberger, Learning driver-response relationships from synchronization patterns, Physical Review E, vol.61, issue.5, 2000.
DOI : 10.1103/PhysRevE.61.5142

A. Schmitz, Measuring statistical dependence and coupling of subsystems, Physical Review E, vol.62, issue.5, 2000.
DOI : 10.1103/PhysRevE.62.7508

E. Pereda, R. Rial, A. Gamundi, and J. Gonzalez, Assessment of changing interdependencies between human electroencephalograms using nonlinear methods, Physica D: Nonlinear Phenomena, vol.148, issue.1-2, pp.147-158, 2001.
DOI : 10.1016/S0167-2789(00)00190-1

C. J. Stam and B. W. Van-dijk, Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets, Physica D: Nonlinear Phenomena, vol.163, issue.3-4, pp.236-251, 2002.
DOI : 10.1016/S0167-2789(01)00386-4

J. Theiler, Spurious dimension from correlation algorithms applied to limited time-series data, Physical Review A, vol.34, issue.3, pp.2427-2432, 1986.
DOI : 10.1103/PhysRevA.34.2427

P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D: Nonlinear Phenomena, vol.9, issue.1-2, pp.189-208, 1983.
DOI : 10.1016/0167-2789(83)90298-1

C. J. Stam, T. Montez, B. F. Jones, S. A. Rombouts, Y. Van-der-made et al., Disturbed fluctuations of resting state EEG synchronization in Alzheimer's disease, Clinical Neurophysiology, vol.116, issue.3, pp.708-715, 2005.
DOI : 10.1016/j.clinph.2004.09.022

R. Ferri, C. J. Stam, B. Lanuzza, F. I. Cosentino, M. Elia et al., Different EEG frequency band synchronization during nocturnal frontal lobe seizures, Clinical Neurophysiology, vol.115, issue.5, pp.1202-1211, 2004.
DOI : 10.1016/j.clinph.2003.12.014

J. Altenburg, R. J. Vermeulen, R. L. Strijers, W. P. Fetter, and C. J. Stam, Seizure detection in the neonatal EEG with synchronization likelihood, Clinical Neurophysiology, vol.114, issue.1, pp.50-55, 2003.
DOI : 10.1016/S1388-2457(02)00322-X

M. Dumont, F. Jurysta, J. Lanquart, P. Migeotte, P. Van-de-borne et al., Interdependency between heart rate variability and sleep EEG: linear/non-linear?, Clinical Neurophysiology, vol.115, issue.9, pp.2031-2040, 2004.
DOI : 10.1016/j.clinph.2004.04.007

K. Ansari-asl, L. Senhadji, F. Wendling, and J. J. Bellanger, Quantitative comparison of signal analysis methods for charactrization of brain functional conectivity, 3rd European Medical and Biological Engineering Conference EMBEC'05, 2005.

K. Ansari-asl, L. Senhadji, J. Bellanger, and F. Wendling, Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals, Physical Review E, vol.74, issue.3, 2005.
DOI : 10.1103/PhysRevE.74.031916

URL : https://hal.archives-ouvertes.fr/inserm-00129780

J. H. Martin, The collective electrical behavior of cortical neurons: the electroencephalogram and the mechanisms of epilepsy, Principles of neural science, pp.777-791, 1991.

J. P. Pijn, J. Van-neerven, A. Noest, F. H. Lopes, and . Silva, Chaos or noise in EEG signals; dependence on state and brain site, Electroencephalography and Clinical Neurophysiology, vol.79, issue.5, pp.371-81, 1991.
DOI : 10.1016/0013-4694(91)90202-F

S. N. Sarbadhikari and K. Chakrabarty, Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization, Medical Engineering & Physics, vol.23, issue.7, pp.445-55, 2001.
DOI : 10.1016/S1350-4533(01)00075-3

P. Faure and H. Korn, Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation, Comptes Rendus de l'Acad??mie des Sciences - Series III - Sciences de la Vie, vol.324, issue.9, pp.773-93, 2001.
DOI : 10.1016/S0764-4469(01)01377-4

A. Babloyantz and C. Lourenco, BRAIN CHAOS AND COMPUTATION, International Journal of Neural Systems, vol.07, issue.04, pp.461-71, 1996.
DOI : 10.1142/S0129065796000440

N. Birbaumer, H. Flor, W. Lutzenberger, and T. Elbert, Chaos and order in the human brain, Electroencephalogr Clin Neurophysiol, vol.44, pp.450-459, 1995.

J. Horgan, Brain storm Controlling chaos could help treat epilepsy, Sci Am, vol.271, p.24, 1994.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano et al., Controlling chaos in the brain, Nature, vol.370, issue.6491, pp.615-635, 1994.
DOI : 10.1038/370615a0

W. S. Pritchard and D. W. Duke, Measuring Chaos in the Brain: A Tutorial Review of Nonlinear Dynamical Eeg Analysis, International Journal of Neuroscience, vol.16, issue.1-4, pp.31-80, 1992.
DOI : 10.1080/17470216008416732

K. Ansari-asl, F. Wendling, J. J. Bellanger, and L. Senhadji, Comparison of two estimators of time-frequency interdependencies between nonstationary signals: application to epileptic EEG, The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp.263-266, 2004.
DOI : 10.1109/IEMBS.2004.1403142

URL : https://hal.archives-ouvertes.fr/inserm-00129781

M. Hénon, A two-dimensional mapping with a strange attractor, Communications in Mathematical Physics, vol.20, issue.1, pp.69-77, 1976.
DOI : 10.1007/BF01608556

J. Bhattacharya, E. Pereda, and H. Petsche, Effective detection of coupling in short and noisy bivariate data, IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), vol.33, issue.1, pp.85-95, 2003.
DOI : 10.1109/TSMCB.2003.808175

G. Osipov, A. Pikovsky, M. Rosenblum, and J. Kurths, Phase synchronization effects in a lattice of nonidentical R??ssler oscillators, Physical Review E, vol.55, issue.3, pp.2353-2361, 1997.
DOI : 10.1103/PhysRevE.55.2353

L. Brunnet, H. Chate, and P. Manneville, Long-range order with local chaos in lattices of diffusively coupled ODEs, Physica D: Nonlinear Phenomena, vol.78, issue.3-4, pp.141-154, 1994.
DOI : 10.1016/0167-2789(94)90111-2

O. E. Rossler, An equation for continuous chaos, Physics Letters A, vol.57, issue.5, pp.397-398, 1976.
DOI : 10.1016/0375-9601(76)90101-8

W. J. Freeman, Models of the dynamics of neural populations, Electroencephalogr Clin Neurophysiol, pp.9-18, 1978.

W. J. Freeman, Simulation of chaotic EEG patterns with a dynamic model of the olfactory system, Biological Cybernetics, vol.52, issue.2-3, pp.139-50, 1987.
DOI : 10.1007/BF00317988

F. H. Eeckman and W. J. Freeman, Asymmetric sigmoid non-linearity in the rat olfactory system, Brain Research, vol.557, issue.1-2, pp.13-21, 1991.
DOI : 10.1016/0006-8993(91)90110-H

F. H. Lopes-da-silva, A. Hoeks, H. Smits, and L. H. Zetterberg, Model of brain rhythmic activity, Kybernetik, vol.1, issue.1, pp.27-37, 1974.
DOI : 10.1007/BF00270757

L. H. Zetterberg, L. Kristiansson, and K. Mossberg, Performance of a model for a local neuron population, Biological Cybernetics, vol.1, issue.1, pp.15-26, 1978.
DOI : 10.1007/BF00337367

L. S. Leung, Nonlinear feedback model of neuronal populations in hippocampal CAl region, J Neurophysiol, vol.47, pp.845-68, 1982.

B. H. Jansen and V. G. Rit, Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, Biological Cybernetics, vol.580, issue.4, pp.357-66, 1995.
DOI : 10.1007/BF00199471

B. H. Jansen, G. Zouridakis, and M. E. Brandt, A neurophysiologically-based mathematical model of flash visual evoked potentials, Biological Cybernetics, vol.31, issue.3, pp.275-83, 1993.
DOI : 10.1007/BF00224863

F. Wendling, J. J. Bellanger, F. Bartolomei, and P. Chauvel, Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals, Biological Cybernetics, vol.83, issue.4, pp.367-78, 2000.
DOI : 10.1007/s004220000160

F. Wendling, F. Bartolomei, J. J. Bellanger, and P. Chauvel, Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition, European Journal of Neuroscience, vol.38, issue.9, pp.1499-508, 2002.
DOI : 10.1007/s004220050191

J. L. Hernandez, P. A. Valdes, and P. Vila, EEG spike and wave modelled by a stochastic limit cycle, NeuroReport, vol.7, issue.13, pp.2246-50, 1996.
DOI : 10.1097/00001756-199609020-00037

H. Sugimoto, N. Ishii, A. Iwata, and N. Suzumura, Stationarity and normality test for biomedical data, Computer Programs in Biomedicine, vol.7, issue.4, pp.293-304, 1977.
DOI : 10.1016/0010-468X(77)90045-9

H. Sugimoto, N. Ishii, A. Iwata, N. Suzumura, and T. Tomita, On the stationarity and normality of the electroencephalographic data during sleep stages, Computer Programs in Biomedicine, vol.8, issue.3-4, pp.224-258, 1978.
DOI : 10.1016/0010-468X(78)90029-6

F. H. Lopes-da and . Silva, Analysis of EEG non-stationarities, Electroencephalogr Clin Neurophysiol, pp.163-79, 1978.

S. J. Schiff, D. Colella, G. M. Jacyna, E. Hughes, J. W. Creekmore et al., Brain chirps: spectrographic signatures of epileptic seizures, Clinical Neurophysiology, vol.111, issue.6, pp.953-961, 2000.
DOI : 10.1016/S1388-2457(00)00259-5

M. B. Shamsollahi, Contribution à l'analyse temps-fréquence des signaux stéréoélectroencéphalographiques et phonocardiographiques, Rennes: Université de Rennes, vol.1, 1997.

L. Cohen, Time-frequency analysis, 1995.

B. Boashash, Time frequency signal analysis and processing : a comprehensive reference, 2003.

B. Boashash, Time-Frequency Signal Analysis: Methods and Applications., Biometrics, vol.49, issue.4, 1992.
DOI : 10.2307/2532288

F. Wendling, M. B. Shamsollahi, J. M. Badier, and J. J. Bellanger, Time-frequency matching of warped depth-EEG seizure observations, IEEE Transactions on Biomedical Engineering, vol.46, issue.5, pp.601-606, 1999.
DOI : 10.1109/10.759060

L. Senhadji and F. Wendling, Epileptic transient detection: wavelets and time-frequency approaches, Neurophysiologie Clinique/Clinical Neurophysiology, vol.32, issue.3, pp.175-192, 2002.
DOI : 10.1016/S0987-7053(02)00304-0

URL : https://hal.archives-ouvertes.fr/inserm-00130050

P. J. Durka and K. J. Blinowska, A unified time-frequency parametrization of EEGs, IEEE Engineering in Medicine and Biology Magazine, vol.20, issue.5, pp.47-53, 2001.
DOI : 10.1109/51.956819

P. Celka, B. Boashash, and P. Colditz, Preprocessing and time-frequency analysis of newborn EEG seizures, IEEE Engineering in Medicine and Biology Magazine, vol.20, issue.5, pp.30-39, 2001.
DOI : 10.1109/51.956817

M. B. Priestley, Non-linear and non-stationary time series analysis, 1988.

L. A. Zadeh, Frequency Analysis of Variable Networks, Proceedings of the IRE, vol.38, issue.3, pp.291-299, 1950.
DOI : 10.1109/JRPROC.1950.231083

J. Lachaux, A. Lutz, D. Rudrauf, D. Cosmelli, M. L. Van-quyen et al., Estimating the time-course of coherence between single-trial brain signals: an introduction to wavelet coherence, Neurophysiologie Clinique/Clinical Neurophysiology, vol.32, issue.3, pp.157-174, 2002.
DOI : 10.1016/S0987-7053(02)00301-5

P. Wahlberg and G. Lantz, Approximate Time-Variable Coherence Analysis of Multichannel Signals, Multidimensional Systems and Signal Processing, pp.237-264, 2002.

Y. Shin, D. Gobert, S. Sung, E. J. Powers, and J. B. Park, Application of Cross Time-Frequency Analysis to Postural Sway Behavior: The Effects of Aging and Visual Systems, IEEE Transactions on Biomedical Engineering, vol.52, issue.5, pp.859-868, 2005.
DOI : 10.1109/TBME.2005.844278

L. B. White and B. Boashash, Cross spectral analysis of nonstationary processes Information Theory, IEEE Transactions on, vol.36, pp.830-835, 1990.

G. Matz and F. Hlawatsch, Time-frequency coherence analysis of nonstationary random processes, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496), pp.554-558, 2000.
DOI : 10.1109/SSAP.2000.870186

P. Flandrin, On the positivity of the Wigner-Ville spectrum, Signal Processing, vol.11, issue.2, pp.187-189, 1986.
DOI : 10.1016/0165-1684(86)90037-X

R. Manuca, M. C. Casdagli, and R. S. Savit, Nonstationarity in epileptic EEG and implications for neural dynamics, Mathematical Biosciences, vol.147, issue.1, pp.1-22, 1998.
DOI : 10.1016/S0025-5564(97)00055-2

K. Müller, G. Lohmann, J. Neumann, M. Grigutsch, T. Mildner et al., Investigating the wavelet coherence phase of the BOLD signal, Journal of Magnetic Resonance Imaging, vol.10, issue.1, pp.145-152, 2004.
DOI : 10.1002/jmri.20064

B. Cazelles, M. Chavez, A. J. Mcmichael, and S. Hales, Nonstationary Influence of El Ni??o on the Synchronous Dengue Epidemics in Thailand, PLoS Medicine, vol.4, issue.4, p.106, 2005.
DOI : 10.1371/journal.pmed.0020106.sg004

J. A. Sills and E. W. Kamen, On some classes of nonstationary parametric processes, Journal of the Franklin Institute, vol.337, issue.2-3, pp.217-249, 2000.
DOI : 10.1016/S0016-0032(00)00018-1

G. E. Box and G. M. Jenkins, Time series analysis : forecasting and control, Rev, 1976.
DOI : 10.1002/9781118619193

Y. Grenier, Time-dependent ARMA modeling of nonstationary signals, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.31, issue.4, pp.899-911, 1983.
DOI : 10.1109/TASSP.1983.1164152

S. M. Kay, Modern spectral estimation : theory and application, 1988.

P. Flandrin, Temps-fréquence, 1998.

A. Kaderli and A. S. Kayhan, A spectral matching approach for parameter and spectral estimation of nonstationary rational processes, Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, pp.2223-2231, 2001.
DOI : 10.1109/78.950778

Y. Xu, S. Haykin, and R. J. Racine, Multiple window time-frequency distribution and coherence of EEG using Slepian sequences and Hermite functions, Biomedical Engineering IEEE Transactions on, vol.46, pp.861-866, 1999.

A. S. Kayhan, A. El-jaroudi, and L. F. Chaparro, Evolutionary periodogram for nonstationary signals, Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, pp.1527-1536, 1994.
DOI : 10.1109/78.286968

P. Flandrin and B. Escudié, Principe et mise en oeuvre de l'analyse temps-fréquence par transformation de Wigner-Ville, Traitement du Signal, vol.2, pp.143-151, 1985.

A. Kaderli and A. S. Kayhan, Spectral estimation of nonstationary ARMA processes using the evolutionary cepstrum, IEEE Signal Processing Letters, vol.9, issue.4, pp.130-132, 2002.
DOI : 10.1109/97.1001650

R. Zou and K. H. Chon, Robust Algorithm for Estimation of Time-Varying Transfer Functions, IEEE Transactions on Biomedical Engineering, vol.51, issue.2, pp.219-228, 2004.
DOI : 10.1109/TBME.2003.820381

H. Zhao, R. Zou, and K. H. Chon, Estimation of Time-Varying Coherence Function Using Time-Varying Transfer Functions, Conference Proceedings. 26th Annual International Conference of the, pp.298-301, 2004.
DOI : 10.1007/s10439-005-7045-4

B. Schack, G. Grieszbach, and W. Krause, The sensitivity of instantaneous coherence for considering elementary comparison processing. Part I: the relationship between mental activities and instantaneous EEG coherence, International Journal of Psychophysiology, vol.31, issue.3, pp.219-240, 1999.
DOI : 10.1016/S0167-8760(98)00052-X

B. Schack, G. Grieszbach, H. Nowak, and W. Krause, The sensitivity of instantaneous coherence for considering elementary comparison processing. Part II: similarities and differences between EEG and MEG coherences, International Journal of Psychophysiology, vol.31, issue.3, pp.241-259, 1999.
DOI : 10.1016/S0167-8760(98)00053-1

H. P. Zaveri, W. J. Williams, J. C. Sackellares, A. Beydoun, R. B. Duckrow et al., Measuring the coherence of intracranial electroencephalograms, Clinical Neurophysiology, vol.110, issue.10, pp.1717-1742, 1999.
DOI : 10.1016/S1388-2457(99)00136-4

O. M. Razoumnikova, Functional organization of different brain areas during convergent and divergent thinking: an EEG investigation, Cognitive Brain Research, vol.10, issue.1-2, pp.11-18, 2000.
DOI : 10.1016/S0926-6410(00)00017-3

A. R. Nikolaev, G. A. Ivanitsky, A. M. Ivanitsky, M. I. Posner, and Y. G. Abdullaev, Correlation of brain rhythms between frontal and left temporal (Wernicke???s) cortical areas during verbal thinking, Neuroscience Letters, vol.298, issue.2, pp.107-110, 2001.
DOI : 10.1016/S0304-3940(00)01740-7

K. Ansari-asl, F. Wendling, J. J. Bellanger, and L. Senhadji, Suivi de relation en temps et en fréquence dans les signaux SEEG épileptiques. Evaluation de deux estimateurs linéaires, GRETSI, pp.281-284, 2003.

K. Ansari-asl, J. Bellanger, F. Bartolomei, F. Wendling, and L. Senhadji, Time-Frequency Characterization of Interdependencies in Nonstationary Signals: Application to Epileptic EEG, IEEE Transactions on Biomedical Engineering, vol.52, issue.7, pp.1218-1226, 2005.
DOI : 10.1109/TBME.2005.847541

URL : https://hal.archives-ouvertes.fr/inserm-00130426

T. Schreiber and A. Schmitz, Surrogate time series, Physica D: Nonlinear Phenomena, vol.142, issue.3-4, pp.346-382, 2000.
DOI : 10.1016/S0167-2789(00)00043-9

P. Celka, Neuronal coordination in the brain: A signal processing perspective, Signal Processing, vol.85, issue.11, pp.2063-2064, 2005.
DOI : 10.1016/j.sigpro.2005.07.001

T. I. Netoff, L. M. Pecora, and S. J. Schiff, Analytical coupling detection in the presence of noise and nonlinearity, Physical Review E, vol.69, issue.1, pp.17201-17205, 2004.
DOI : 10.1103/PhysRevE.69.017201

L. Ljung, System identification : theory for the user, NJ, 1999.

B. Friedlander and B. Porat, A spectral matching technique for ARMA parameter estimation, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.32, issue.2, pp.338-343, 1984.
DOI : 10.1109/TASSP.1984.1164328

D. G. Luenberger, Linear and nonlinear programming, Boston: Kluwer Academic, vol.228, 2003.
DOI : 10.1007/978-3-319-18842-3

M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear programming : theory and algorithms, 1993.
DOI : 10.1002/0471787779

J. Deller and J. , Deterministic models for a certain class of autoregressive equations with stochastic coefficients, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.29, issue.2, pp.312-315, 1981.
DOI : 10.1109/TASSP.1981.1163548

S. Lu, K. H. Ju, and K. H. Chon, A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry, Biomedical Engineering IEEE Transactions on, vol.48, pp.1116-1124, 2001.

K. H. Chon, H. Zhao, R. Zou, and K. Ju, Multiple Time-Varying Dynamic Analysis Using Multiple Sets of Basis Functions, IEEE Transactions on Biomedical Engineering, vol.52, issue.5, pp.956-60, 2005.
DOI : 10.1109/TBME.2005.845362

S. S. Haykin, Adaptive filter theory, 1996.

J. G. Proakis and D. G. Manolakis, Digital signal processing, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.23, issue.4, 1996.
DOI : 10.1109/TASSP.1975.1162707