D. H. Abney, A. Paxton, R. Dale, and C. T. Kello, Complexity matching in dyadic conversation, Journal of Experimental Psychology: General, vol.143, issue.6, pp.2304-2315, 2014.

Z. M. Almurad and D. Delignières, Evenly spacing in Detrended Fluctuation Analysis, Physica A: Statistical Mechanics and Its Applications, vol.451, pp.63-69, 2016.


Z. M. Almurad, C. Roume, H. Blain, and D. Delignières, Complexity Matching : Restoring the Complexity of Locomotion in Older People Through Arm-in-Arm Walking, Frontiers in Physiology, vol.9, p.1766, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01976776


Z. M. Almurad, C. Roume, and D. Delignières, Complexity matching in sideby-side walking, Human Movement Science, vol.54, pp.125-136, 2017.


G. Aquino, M. Bologna, P. Grigolini, and B. J. West, Publisher's Note : Beyond the Death of Linear Response: 1 / f Optimal Information Transport, 2010.

. Lett, , vol.105, p.40601, 2010.

, Physical Review Letters, vol.105, issue.6, p.69901

G. Aquino, M. Bologna, B. J. West, and P. Grigolini, Transmission of information between complex systems : 1 / f resonance, Physical Review E, vol.83, issue.5, p.51130, 2011.

H. Atlan, Le vivant post-génomique, ou, Qu'est-ce que l'auto-organisation, 2011.

R. Balocchi, M. Varanini, and A. Macerata, Quantifying different degrees of coupling in detrended cross-correlation analysis, Europhysics Letters), vol.101, issue.2, 2013.

B. C. Beltz, C. T. Kello, and . Vanchevsky, On the Intrinsic Fluctuations of Human Behavior, Focus on Cognitive Psychology Research, pp.25-41, 2006.

J. Beran, Long-memory processes, Probabilistic properties and statistical methods, 2013.

S. M. Boker, J. L. Rotondo, M. Xu, and K. King, Windowed cross-correlation and peak picking for the analysis of variability in the association between behavioral time series, Psychological Methods, vol.7, issue.3, pp.338-355, 2002.


K. Burrage, I. Lenane, and G. Lythe, Numerical Methods for Second-Order Stochastic Differential Equations, SIAM Journal on Scientific Computing, vol.29, issue.1, pp.245-264, 2007.

D. C. Caccia, D. Percival, M. J. Cannon, G. Raymond, and J. B. Bassingthwaighte, Analyzing exact fractal time series : Evaluating dispersional analysis and rescaled range methods, Physica A: Statistical Mechanics and Its Applications, vol.246, issue.3-4, pp.609-632, 1997.

M. J. Cannon, D. B. Percival, D. C. Caccia, G. M. Raymond, and J. B. Bassingthwaighte, Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series, Physica A: Statistical Mechanics and Its Applications, vol.241, issue.3-4, pp.606-626, 1997.

Y. Chen, M. Ding, and J. A. Scott-kelso, Origins of Timing Errors in Human Sensorimotor Coordination, Journal of Motor Behavior, vol.33, issue.1, pp.3-8, 2001.


Y. Chen, B. H. Repp, and A. D. Patel, Spectral decomposition of variability in synchronization and continuation tapping : Comparisons between auditory and visual pacing and feedback conditions, Human Movement Science, vol.21, issue.4, pp.515-532, 2002.

J. Correll, 1/f noise and effort on implicit measures of bias, Journal of Personality and Social Psychology, vol.94, issue.1, pp.48-59, 2008.

P. F. Craigmile, Simulating a class of stationary Gaussian processes using the Davies-Harte algorithm, with application to long memory processes, Journal of Time Series Analysis, vol.24, issue.5, pp.505-511, 2003.

R. B. Davies and D. S. Harte, Tests for Hurst effect, Biometrika, vol.74, issue.1, pp.95-101, 1987.

D. Delignières, Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Mathematical Problems in Engineering, vol.485623, 2015.

D. Delignières and V. Marmelat, Degeneracy and long-range correlations, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.23, issue.4, 2013.

D. Delignieres, S. Ramdani, L. Lemoine, K. Torre, M. Fortes et al., , 2006.

, Fractal analyses for 'short' time series : A re-assessment of classical methods, Journal of Mathematical Psychology, vol.50, issue.6, pp.525-544


. Delignières, A. Didier, Z. M. Roume, C. Marmelat, and V. , Multifractal signatures of complexity matching, Experimental Brain Research, 2016.


. Delignières, . Didier, L. Lemoine, and K. Torre, Time intervals production in tapping and oscillatory motion, Human Movement Science, vol.23, issue.2, pp.87-103, 2004.


D. Delignières and V. Marmelat, Strong anticipation and long-range crosscorrelation : Application of detrended cross-correlation analysis to human behavioral data, Physica A: Statistical Mechanics and Its Applications, vol.394, pp.47-60, 2014.

. Delignières, T. Didier, K. Bernard, and P. , Transition from Persistent to Anti-Persistent Correlations in Postural Sway Indicates Velocity-Based Control, PLoS Computational Biology, vol.7, issue.2, p.1001089, 2011.


. Delignières, T. Didier, K. Lemoine, and L. , Fractal models for event-based and dynamical timers, Acta Psychologica, vol.127, issue.2, pp.382-397, 2008.


. Delignières, T. Didier, K. Lemoine, and L. , Long-Range Correlation in Synchronization and Syncopation Tapping : A Linear Phase Correction Model, 2009.

, PLoS ONE, vol.4, issue.11

C. Diebolt and V. Guiraud, A Note On Long Memory Time Series, Quality & Quantity, vol.39, issue.6, pp.827-836, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00278694

D. M. Dubois, Mathematical Foundations of Discrete and Functional Systems with Strong and Weak Anticipations, Anticipatory Behavior in Adaptive Learning Systems, vol.2684, pp.110-132, 2003.


A. Eke, P. Hermán, J. Bassingthwaighte, G. Raymond, D. Percival et al., Physiological time series : Distinguishing fractal noises from motions, Pflügers Archiv -European Journal of Physiology, vol.439, issue.4, pp.403-415, 2000.


A. Eke, P. Herman, L. Kocsis, and L. R. Kozak, Fractal characterization of complexity in temporal physiological signals, Physiological Measurement, vol.23, issue.1, pp.1-38, 2002.

J. M. Fine, A. D. Likens, E. L. Amazeen, and P. G. Amazeen, Emergent complexity matching in interpersonal coordination : Local dynamics and global variability, Journal of Experimental Psychology: Human Perception and Performance, vol.41, issue.3, pp.723-737, 2015.

P. M. Fitts, The information capacity of the human motor system in controlling the amplitude of movement, Journal of Experimental Psychology, vol.47, issue.6, pp.381-391, 1954.

P. F. Fougere, On the accuracy of spectrum analysis of red noise processes using maximum entropy and periodogram methods : Simulation studies and application to geophysical data, Journal of Geophysical Research, vol.90, issue.A5, p.4355, 1985.

D. L. Gilden, T. Thornton, and M. W. Mallon, 1/f noise in human cognition, Science, vol.267, issue.5205, pp.1837-1839, 1995.

A. L. Goldberger, L. A. Amaral, J. M. Hausdorff, P. C. Ivanov, C. Peng et al., Fractal dynamics in physiology : Alterations with disease and aging, Proceedings of the National Academy of Sciences, vol.99, pp.2466-2472, 2002.

T. Graves, R. Gramacy, N. Watkins, and C. Franzke, A Brief History of Long Memory : Hurst, Mandelbrot and the Road to ARFIMA, Entropy, vol.19, issue.9, p.437, 1951.

H. Haken, J. A. Kelso, and H. Bunz, A theoretical model of phase transitions in human hand movements, Biological Cybernetics, vol.51, issue.5, pp.347-356, 1985.


J. M. Hausdorff, S. L. Mitchell, R. Firtion, C. K. Peng, M. E. Cudkowicz et al., Altered fractal dynamics of gait : Reduced strideinterval correlations with aging and Huntington's disease, Journal of Applied Physiology, vol.82, issue.1, pp.262-269, 1985.

J. M. Hausdorff, C. K. Peng, Z. Ladin, J. Y. Wei, and A. L. Goldberger, Is walking a random walk? Evidence for long-range correlations in stride interval of human gait, Journal of Applied Physiology, vol.78, issue.1, pp.349-358, 1995.


J. M. Hausdorff, P. L. Purdon, C. K. Peng, Z. Ladin, J. Y. Wei et al., Fractal dynamics of human gait : Stability of long-range correlations in stride interval fluctuations, Journal of Applied Physiology, vol.80, issue.5, pp.1448-1457, 1996.


N. Hunt, D. Mcgrath, and N. Stergiou, The influence of auditory-motor coupling on fractal dynamics in human gait, Scientific Reports, vol.4, issue.1, p.5879, 2015.

E. A. Ihlen and B. Vereijken, Interaction-dominant dynamics in human cognition : Beyond 1/?? fluctuation, Journal of Experimental Psychology: General, vol.139, issue.3, pp.436-463, 2010.

R. Jennane, R. Harba, and G. Jacquet, Méthodes d'analyse du mouvement brownien fractionnaire : Théorie et résultats comparatifs, Traitement du Signal, vol.18, issue.5-6, pp.419-436, 2001.

J. P. Kaipust, D. Mcgrath, M. Mukherjee, and N. Stergiou, Gait Variability is Altered in Older Adults When Listening to Auditory Stimuli with Differing Temporal Structures, Annals of Biomedical Engineering, vol.41, issue.8, pp.1595-1603, 2013.


J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-bunde, S. Havlin, A. Bunde et al., Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and its Applications, vol.316, issue.1, pp.87-114, 2002.

I. Konvalinka, P. Vuust, A. Roepstorff, and C. D. Frith, Follow you, follow me : Continuous mutual prediction and adaptation in joint tapping, The Quarterly Journal of Experimental Psychology, vol.63, issue.11, pp.2220-2230, 2010.


L. Lemoine and D. Delignières, Detrended Windowed (lag one) Autocorrelation : A new Method for Distinguishing between Event-Based and Emergent Timing, 2009.

, Quarterly Journal of Experimental Psychology, vol.62, issue.3, pp.585-604


J. J. Liddy and J. M. Haddad, Evenly spaced Detrended Fluctuation Analysis : Selecting the number of points for the diffusion plot, Physica A: Statistical Mechanics and Its Applications, vol.491, pp.233-248, 2018.


G. Madison, Timing of Action During and After Synchronization With Linearly Changing Intervals, An Interdisciplinary Journal, vol.22, issue.3, pp.441-459, 2005.

K. Mahmoodi, B. J. West, and P. Grigolini, On the Dynamical Foundation of Multifractality, 2017.

K. Mahmoodi, B. J. West, and P. Grigolini, Complexity Matching and Requisite Variety, 2018.

D. Makowiec, A. Rynkiewicz, R. Ga?aska, J. Wdowczyk-szulc, and M. ?arczy?ska-buchowiecka, Reading multifractal spectra : Aging by multifractal analysis of heart rate, Europhysics Letters), vol.94, issue.6, p.68005, 2011.

V. Marmelat and D. Delignières, Strong anticipation : Complexity matching in interpersonal coordination, Experimental Brain Research, vol.222, issue.1-2, pp.137-148, 2012.


V. Marmelat, K. Torre, P. J. Beek, and A. Daffertshofer, Persistent Fluctuations in Stride Intervals under Fractal Auditory Stimulation, PLoS ONE, vol.9, issue.3, 2014.

E. Morin, Introduction à la pensée complexe, 2014.

P. Mukli, Z. Nagy, and A. Eke, Multifractal formalism by enforcing the universal behavior of scaling functions, Physica A: Statistical Mechanics and Its Applications, vol.417, pp.150-167, 2015.

D. Nourrit-lucas, A. O. Tossa, G. Zélic, and D. Delignières, Learning, Motor Skill, and Long-Range Correlations, Journal of Motor Behavior, vol.47, issue.3, pp.182-189, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00948236


L. Nowicki, W. Prinz, M. Grosjean, B. H. Repp, and P. E. Keller, Mutual adaptive timing in interpersonal action coordination, vol.23, pp.6-20, 2013.

P. O?wi?cimka, J. Kwapie?, and S. Dro?d?, Wavelet versus detrended fluctuation analysis of multifractal structures, Physical Review E, vol.74, issue.1, p.16103, 2006.

N. Pecenka and P. E. Keller, The role of temporal prediction abilities in interpersonal sensorimotor synchronization, Experimental Brain Research, vol.211, issue.3-4, pp.505-515, 2011.

H. Peitgen, D. Saupe, and M. F. Barnsley, The Science of fractal images, 1988.

C. K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley et al., Long-range anticorrelations and non-Gaussian behavior of the heartbeat, Physical Review Letters, vol.70, issue.9, pp.1343-1346, 1993.

C. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley et al., Mosaic organization of DNA nucleotides, Physical Review E, vol.49, issue.2, pp.1685-1689, 1994.

B. Podobnik and H. E. Stanley, Detrended Cross-Correlation Analysis : A New Method for Analyzing Two Nonstationary Time Series, Physical Review Letters, vol.100, issue.8, p.84102, 2008.

J. Pressing and G. Jolley-rogers, Spectral properties of human cognition and skill, Biological Cybernetics, vol.76, issue.5, pp.339-347, 1997.

G. Rangarajan and M. Ding, Integrated approach to the assessment of long range correlation in time series data, Physical Review E, issue.5, pp.4991-5001, 2000.


S. K. Rankin and C. J. Limb, Auditory-motor synchronization with temporally fluctuating sequences is dependent on fractal structure but not musical expertise, Frontiers in Psychology, 2014.

B. H. Repp, Sensorimotor synchronization : A review of the tapping literature, Psychonomic Bulletin & Review, vol.12, issue.6, pp.969-992, 2005.


B. H. Repp and Y. Su, Sensorimotor synchronization : A review of recent research, Psychonomic Bulletin & Review, vol.20, issue.3, pp.403-452, 2006.


D. C. Richardson and R. Dale, Looking To Understand : The Coupling Between Speakers' and Listeners' Eye Movements and Its Relationship to Discourse Comprehension, Cognitive Science, vol.29, issue.6, pp.1045-1060, 2005.


M. J. Richardson, K. L. Marsh, R. W. Isenhower, J. R. Goodman, and R. C. Schmidt, Rocking together : Dynamics of intentional and unintentional interpersonal coordination, Human Movement Science, vol.26, issue.6, pp.867-891, 2007.


R. Rosen, Essays on life itself, 2000.

C. Roume, Z. M. Almurad, M. Scotti, S. Ezzina, H. Blain et al., , 2018.

, Windowed detrended cross-correlation analysis of synchronization processes, Physica A: Statistical Mechanics and Its Applications, vol.503, pp.1131-1150


C. Roume, S. Ezzina, H. Blain, and D. Delignieres, Biases in the Simulation and Analysis of Fractal Processes, Computational and Mathematical Methods in Medicine, p.14, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02417699

R. C. Schmidt, M. Bienvenu, P. A. Fitzpatrick, and P. G. Amazeen, A comparison of intra-and interpersonal interlimb coordination : Coordination breakdowns and coupling strength, Journal of Experimental Psychology. Human Perception and Performance, vol.24, issue.3, pp.884-900, 1998.

R. C. Schmidt, C. Carello, and M. T. Turvey, Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people, Journal of Experimental Psychology: Human Perception and Performance, vol.16, issue.2, pp.227-247, 1990.

G. Schöner, H. Haken, and J. A. Kelso, A stochastic theory of phase transitions in human hand movement, Biological Cybernetics, vol.53, issue.4, pp.247-257, 1986.


A. Y. Schumann and J. W. Kantelhardt, Multifractal moving average analysis and test of multifractal model with tuned correlations, Physica A: Statistical Mechanics and Its Applications, vol.390, issue.14, pp.2637-2654, 2011.


K. Shockley, D. C. Richardson, and R. Dale, Conversation and Coordinative Structures, Topics in Cognitive Science, vol.1, issue.2, pp.305-319, 2009.


A. B. Slifkin and J. R. Eder, Amplitude requirements, visual information, and the spatial structure of movement, Experimental Brain Research, vol.220, issue.3-4, pp.297-310, 2012.


A. B. Slifkin and J. R. Eder, Fitts' index of difficulty predicts the 1/f structure of movement amplitude time series, Experimental Brain Research, vol.232, issue.6, pp.1653-1662, 2014.

T. Stadnitski, Some critical aspects of fractality research, Psychology, and Life Sciences, vol.16, issue.2, pp.137-158, 2012.

D. G. Stephen and J. Anastas, Fractal fluctuations in gaze speed visual search, Perception, & Psychophysics, vol.73, issue.3, pp.666-677, 2011.


D. G. Stephen and J. A. Dixon, Strong anticipation : Multifractal cascade dynamics modulate scaling in synchronization behaviors, Chaos, Solitons & Fractals, vol.44, issue.1-3, pp.160-168, 2011.

N. Stepp and M. T. Turvey, On strong anticipation, Cognitive Systems Research, vol.11, issue.2, pp.148-164, 2010.

M. H. Thaut, B. Tian, and M. R. Azimi-sadjadi, Rhythmic finger tapping to cosine-wave modulated metronome sequences : Evidence of subliminal entrainment, Human Movement Science, vol.17, issue.6, pp.839-863, 1998.

, , pp.31-32

K. Torre and D. Delignières, Distinct ways of timing movements in bimanual coordination tasks : Contribution of serial correlation analysis and implications for modeling, Acta Psychologica, vol.129, issue.2, pp.284-296, 2008.

K. Torre and D. Delignières, Distinct ways of timing movements in bimanual coordination tasks : Contribution of serial correlation analysis and implications for modeling, Acta Psychologica, vol.129, issue.2, pp.284-296, 2008.


K. Torre and D. Delignières, Unraveling the finding of 1/f ? noise in selfpaced and synchronized tapping : A unifying mechanistic model, Biological Cybernetics, vol.99, issue.2, pp.159-170, 2008.

K. Torre, D. Delignieres, and L. Lemoine, 1/f ? fluctuations in bimanual coordination : An additional challenge for modeling, Experimental Brain Research, vol.183, issue.2, pp.225-234, 2007.

K. Torre, M. Varlet, and V. Marmelat, Predicting the biological variability of environmental rhythms : Weak or strong anticipation for sensorimotor synchronization?, Brain and Cognition, vol.83, issue.3, pp.342-350, 2013.


G. C. Van-orden, J. G. Holden, and M. T. Turvey, Self-organization of cognitive performance, Journal of Experimental Psychology. General, vol.132, issue.3, pp.331-350, 2003.


V. Neumann, J. Burks, and A. W. , Theory of self-reproducing automata, 1966.

D. Vorberg and A. Wing, Chapter 4 Modeling variability and dependence in timing, Handbook of Perception and Action, vol.2, pp.181-262, 1996.

, , pp.80007-80008

H. U. Voss, Anticipating chaotic synchronization, Physical Review E, vol.61, issue.5, pp.5115-5119, 2000.

E. Wagenmakers, S. Farrell, and R. Ratcliff, Estimation and interpretation of 1/f? noise in human cognition, Psychonomic Bulletin & Review, vol.11, issue.4, pp.579-615, 2004.

T. Warlop, C. Detrembleur, M. Buxes-lopez, G. Stoquart, T. Lejeune et al., Does Nordic Walking restore the temporal organization of gait variability in Parkinson's disease?, Journal of NeuroEngineering and Rehabilitation, vol.14, issue.1, 2017.

B. J. West, E. L. Geneston, and P. Grigolini, Maximizing information exchange between complex networks, Physics Reports, vol.468, issue.1-3, pp.1-99, 2008.


M. L. Wijnants, A. M. Bosman, F. Hasselman, R. F. Cox, and G. C. Van-orden, 1/f scaling in movement time changes with practice in precision aiming, Psychology, and Life Sciences, vol.13, issue.1, pp.79-98, 2009.

A. M. Wing and A. B. Kristofferson, Response delays and the timing of discrete motor responses, Perception & Psychophysics, vol.14, issue.1, pp.5-12, 1973.


J. P. Zbilut, A. Giuliani, and C. L. Webber, Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification, Physics Letters A, vol.246, issue.1-2, pp.122-128, 1998.

G. F. Zebende, DCCA cross-correlation coefficient : Quantifying level of crosscorrelation, Physica A: Statistical Mechanics and Its Applications, vol.390, issue.4, pp.614-618, 2011.