Is There Chaos in the Brain I Concepts of Nonlinear Dynamics and Methods of Investigation英文电子书.pdf

C.R. Acad. Sci. Paris, Sciences de la vie / Life Sciences 324 (2001) 773–793 © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés S0764446901013774/REV Point sur / Concise review Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation Philippe Faure, Henri Korn* Biologie cellulaire et moléculaire du neurone (Inserm V261), Institut Pasteur, 25 rue Docteur Roux, 75724 Paris Cedex 15, France Received 18 June 2001; accepted 2 July 2001 Communicated by Pierre Buser Abstract – In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural assemblies and behavioural patterns, the linkage between them, and their modifications over time, cannot be fully understood in the context of even integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non expert to the fundamental aspects of nonlinear dynamics, the most spectacular aspect of which is chaos theory. After a general history and definition of chaos the principles of analysis of time series in phase space and the general properties of chaotic trajectories will be described as will be the classical measures which allow a process to be classified as chaotic in ideal systems and models. We will then proceed to show how these methods need to be adapted for handling experimental time series; the dangers and pitfalls faced when dealing with non stationary and often noisy data will be stressed, and specific criteria for suspecting determinism in neuronal cells and/or assemblies will be described. We will finally addr