25 présente cette même mesure dans le cas de différentes tailles de réseaux complets unidirectionnels ,
Stochastic synchronization of oscillation in dissipative systems, Radiophysics and Quantum Electronics, vol.89, issue.No. 10, pp.795-802, 1986. ,
DOI : 10.1007/BF01034476
Locally active Hindmarsh???Rose neurons, Chaos, Solitons & Fractals, vol.27, issue.2, pp.405-412, 2006. ,
DOI : 10.1016/j.chaos.2005.04.064
Synchronization of chaos, Encyclopedia of mathematical physics, pp.213-226, 2006. ,
Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems, Physical Review E, vol.62, issue.5, pp.6332-6345, 2000. ,
DOI : 10.1103/PhysRevE.62.6332
Persistent clusters in lattices of coupled nonidentical chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.13, issue.1, pp.165-178, 2003. ,
DOI : 10.1063/1.1514202
Connection graph stability method for synchronized coupled chaotic systems, Physica D: Nonlinear Phenomena, vol.195, issue.1-2, pp.159-187, 2004. ,
DOI : 10.1016/j.physd.2004.03.012
SYNCHRONIZATION AND GRAPH TOPOLOGY, International Journal of Bifurcation and Chaos, vol.15, issue.11, pp.3423-3433, 2005. ,
DOI : 10.1142/S0218127405014143
Synchronization of Bursting Neurons: What Matters in the Network Topology, Physical Review Letters, vol.94, issue.18, p.188101, 2005. ,
DOI : 10.1103/PhysRevLett.94.188101
The synchronization of chaotic systems, Physics Reports, vol.366, issue.1-2, pp.1-101, 2002. ,
DOI : 10.1016/S0370-1573(02)00137-0
Synchronization and Bifurcation in Networks of Coupled Hindmarsh-Rose Neurons, Circuits and Systems, IEEE International Symposium, pp.1541-1544, 2007. ,
Asymptotic dynamics of the slow-fast Hindmarsh-Rose neuronal system, Dynamics of Continuous, Discrete and Impulsive Systemes, Series B : Applications and Algorithms, pp.535-549, 2009. ,
Hopf bifurcation of the slow-fast Hindmarsh-Rose system, sousmis à Nonlinear Analysis : Real World Applications, 2009. ,
Complex emergent properties in synchronized neuronal oscillations From System Complexity to Emergent Properties Understanding Complex Systems series, pp.243-259, 2009. ,
Enhancement of Neural Synchrony by Time Delay, Physical Review Letters, vol.92, issue.7, pp.74104-74105, 2004. ,
DOI : 10.1103/PhysRevLett.92.074104
Bifurcations et chaos, une introduction à la dynamique contemporaine avec des programmes en Pascal, 2000. ,
Estimation of attractors and Synchronization of Generalized Lorenz Systems, Dynamics of Continuous, Discrete and Impulsive Systems, pp.833-852, 2003. ,
Codimension-two bifurcation analysis in Hindmarsh-Rose model with two parameters, Chin. Phy. Lett, vol.22, pp.1325-1328, 2005. ,
GraphStream : A Tool for bridging the gap between Complex Systems and Dynamic Graphs, EPNACS : Emergent Properties in Natural and Artificial Complex Systems, 2007. ,
Synchronous behaviour of two coupled biological neurons, Phys.Rev.Lett, issue.25, pp.815692-5695, 1998. ,
Epilepsy : A comprehensive textbook, Lippincott-Raven, 1975. ,
Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961. ,
DOI : 10.1016/S0006-3495(61)86902-6
Oscillations en biologie, Analyse qualitative et Modèles Collection Mathématiques et Applications SMAI Springer, 2005. ,
DOI : 10.1007/3-540-37670-4
Motor unit and muscle activity in voluntary motor control, Physiol .Rev, vol.63, issue.2, pp.387-436, 1983. ,
Itinerant Dynamics of Class I* Neurons Coupled by Gap Junctions, Lecture Notes in Computer Science, vol.3146, pp.140-160, 2004. ,
DOI : 10.1007/978-3-540-27862-7_8
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
Stability theory of synchronized motion in coupled-oscillator systems III, Prog.Theor.Phys, vol.72, issue.5, pp.885-894, 1984. ,
COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH???ROSE NEURON MODEL, International Journal of Bifurcation and Chaos, vol.17, issue.09, pp.3071-3083, 2007. ,
DOI : 10.1142/S0218127407018877
Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties, Nature, vol.338, issue.6213, pp.334-337, 1989. ,
DOI : 10.1038/338334a0
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2002. ,
Bifurcations in the fast dynamics of neurons : Implications for bursting, pp.1-33, 2004. ,
Bifurcation formulae derived from center manifold theory, Journal of Mathematical Analysis and Applications, vol.63, issue.1, pp.297-312, 1978. ,
DOI : 10.1016/0022-247X(78)90120-8
Theory and Applications of Hopf bifurcation, 1981. ,
Short Wavelength Bifurcations and Size Instabilities in Coupled Oscillator Systems, Physical Review Letters, vol.74, issue.21, pp.4185-4188, 1995. ,
DOI : 10.1103/PhysRevLett.74.4185
Ionic channels of excitable membranes, second edition, Sinauer associates inc, 1992. ,
A model of the nerve impulse using two first-order differential equations, Nature, vol.6, issue.5853, pp.162-164, 1982. ,
DOI : 10.1038/296162a0
A Model of Neuronal Bursting Using Three Coupled First Order Differential Equations, Proc. R. Sc. Lond. B221, pp.87-102, 1984. ,
DOI : 10.1098/rspb.1984.0024
The developpment of the Hindmarsh-Rose model for bursting, chapter 1, Bursting, The genesis of rythm in the nervous system, World Scientific, pp.2-18, 2005. ,
Differential Equations, Dynamical systems and an introduction to chaos, 2003. ,
Spike-train bifurcation scaling in two coupled chaotic neurons, 43] Huygens C. (Hugenii), pp.2108-2110, 1973. ,
DOI : 10.1103/PhysRevE.55.R2108
A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952. ,
DOI : 10.1113/jphysiol.1952.sp004764
Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.17, issue.4, pp.1-043128, 2007. ,
DOI : 10.1063/1.2818153
Which Model to Use for Cortical Spiking Neurons?, IEEE Transactions on Neural Networks, vol.15, issue.5, pp.1063-1070, 2004. ,
DOI : 10.1109/TNN.2004.832719
Dynamical systems in Neuroscience, 2007. ,
Si???lnikov homoclinic orbits in a new chaotic system, Chaos, Solitons & Fractals, vol.32, issue.1, pp.150-159, 2007. ,
DOI : 10.1016/j.chaos.2005.10.088
Mechanisms of phase-locking and frequancy control in pairs of coupled neural oscillators, " Handbook of Dynamical Systems, pp.3-54, 2002. ,
Neuronal pacemaker for breathing visualized in vivo, Nature, vol.400, issue.6742, pp.360-363, 1997. ,
DOI : 10.1038/22540
Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, vol.112, 2004. ,
Local bifurcation of the Chen system, Int. J. Bif. Chaos, vol.12, pp.10-2257, 2002. ,
Some Methods for classification and Analysis of Multivariate Observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, pp.281-297, 1967. ,
Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal, vol.35, issue.1, pp.193-213, 1981. ,
DOI : 10.1016/S0006-3495(81)84782-0
An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of the IRE, vol.50, issue.10, pp.2061-2070, 1962. ,
DOI : 10.1109/JRPROC.1962.288235
An alternative bifurcation analysis of the Rose???Hindmarsh model, Chaos, Solitons & Fractals, vol.23, issue.5, pp.1643-1649, 2005. ,
DOI : 10.1016/S0960-0779(04)00427-8
SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL, International Journal of Bifurcation and Chaos, vol.20, issue.01, 2009. ,
DOI : 10.1142/S0218127410025429
URL : https://hal.archives-ouvertes.fr/hal-00430513
Synchronization in an ensemble of Hindmash-Rose oscillators : using the control-theory in neuroscience, report, 2004. ,
Synchronization in chaotic systems, Physical Review Letters, vol.64, issue.8, pp.821-824, 1990. ,
DOI : 10.1103/PhysRevLett.64.821
Master Stability Functions for Synchronized Coupled Systems, Physical Review Letters, vol.80, issue.10, pp.2109-2112, 1998. ,
DOI : 10.1103/PhysRevLett.80.2109
Dynamic synchronization and chaos in an associative neural network with multiple active memories, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.13, issue.3, pp.1-15, 2003. ,
DOI : 10.1063/1.1602211
A Model of a Thalamic Neuron, Proc. R. Sc. Lond. B225, pp.161-193, 1985. ,
DOI : 10.1098/rspb.1985.0057
Generalized synchronization of chaos in directionally coupled chaotic systems, Physical Review E, vol.51, issue.2, pp.980-994, 1995. ,
DOI : 10.1103/PhysRevE.51.980
Complete synchronization of coupled Hindmarsh-Rose neurons with ring structure, Chineese Review Letter, vol.21, issue.9, pp.1695-1698, 2004. ,
Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons, pp.77-85, 2005. ,
ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY, International Journal of Bifurcation and Chaos, vol.13, issue.11, pp.3325-3340, 2003. ,
DOI : 10.1142/S0218127403008521
Visual Feature Integration and the Temporal Correlation Hypothesis, Annual Review of Neuroscience, vol.18, issue.1, pp.555-586, 1995. ,
DOI : 10.1146/annurev.ne.18.030195.003011
Striving for coherence, Nature, vol.397, issue.6718, pp.391-393, 1999. ,
DOI : 10.1038/17021
Parameter estimation in Hindmarsh-Rose neurons, report, 2006. ,
Impaired odour descriminination on desynchronization of odour-encoding neural assemblies, Nature, issue.6, pp.390-70, 1997. ,
Attention modulates synchronized neuronal firing in primate somatosensory cortex, Nature, vol.80, issue.6774, pp.187-190, 2000. ,
DOI : 10.1038/35004588
Membrane potential synchrony of simultaneously recorded striatal spiny neurons in vivo, Nature, vol.394, issue.6692, pp.475-478, 1998. ,
DOI : 10.1038/28848
CHAOTIC ITINERANCY AS A MECHANISM OF IRREGULAR CHANGES BETWEEN SYNCHRONIZATION AND DESYNCHRONIZATION IN A NEURAL NETWORK, Journal of Integrative Neuroscience, vol.03, issue.02, pp.159-182, 2004. ,
DOI : 10.1142/S021963520400049X
BIFURCATIONS IN TWO-DIMENSIONAL HINDMARSH???ROSE TYPE MODEL, International Journal of Bifurcation and Chaos, vol.17, issue.03, pp.985-998, 2007. ,
DOI : 10.1142/S0218127407017707
Nonlinear Differential Equations and Dynamical Systems, 1996. ,
Complete synchronization in coupled chaotic HR neurons with symmetric coupling schemes, Chineese Review Letter, vol.22, issue.9, pp.2173-2175, 2005. ,
Generalized Q???S (lag, anticipated and complete) synchronization in modified Chua???s circuit and Hindmarsh???Rose systems, Applied Mathematics and Computation, vol.181, issue.1, pp.48-56, 2006. ,
DOI : 10.1016/j.amc.2006.01.017
Chaos Theory Tamed, 1997. ,
On a conjecture regarding the synchronization in an array of linearly coupled dynamical systems, IEEE Transactions on Circuits and Systems I Fundamental theory and Applications, vol.43, pp.161-165, 1996. ,
Generalized synchronization induced by noise and parameter mismatching in Hindmarsh???Rose neurons, Chaos, Solitons & Fractals, vol.23, issue.5, pp.1605-1611, 2005. ,
DOI : 10.1016/S0960-0779(04)00403-5
Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach, Progress of Theoretical Physics, vol.70, issue.5, pp.1240-1248, 1983. ,
DOI : 10.1143/PTP.70.1240
Chaotic synchronization and control in nonlinear-coupled Hindmarsh???Rose neural systems, Chaos, Solitons & Fractals, vol.29, issue.2, pp.342-348, 2006. ,
DOI : 10.1016/j.chaos.2005.08.075
Constructing a new chaotic system based on the S??ilnikov criterion, Chaos, Solitons & Fractals, vol.19, issue.4, pp.985-993, 2004. ,
DOI : 10.1016/S0960-0779(03)00251-0
Hopf bifurcation analysis of the Liu system, Hopf bifurcation of the Liu system, pp.1385-1391, 2008. ,
DOI : 10.1016/j.chaos.2006.09.008
111 M Méthode Connection-graph-stability108 Méthode Master-stability-function ,