Is there chaos in the brain? I. Concepts of nonlinear dynamics and methodsof investigation

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, fir st developed and improved for the physical sciences and engineering, are we ll-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, ne ural assemblies and behavioural patterns, the linkage between them, and the ir modifications overtime, cannot be fully understood in the context of eve n integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non e xpert to the fundamental aspects of nonlinear dynamics, the most spectacula r aspect of which is chaos theory. After a general history and definition o f chaos the principles of analysis of time series in phase space and the ge neral properties of chaotic trajectories will be described as will be the c lassical measures which allow a process to be classified as chaotic in idea l systems and models. We will then proceed to show how these methods need t o be adapted for handling experimental time series; the dangers and pitfall s faced when dealing with non stationary and often noisy data will be stres sed, and specific criteria for suspecting determinism in neuronal cells and /or assemblies will be described. We will finally address two fundamental q uestions, namely i) whether and how can one distinguish, deterministic patt erns from stochastic ones, and, ii) what is the advantage of chaos over ran domness: we will explain why and how the former can be controlled whereas, notoriously, the latter cannot be tamed. In the second paper of the series, results obtained at the level of single cells and their membrane conductan ces in real neuronal networks and in the study of higher brain functions, w ill be critically reviewed. It will be shown that the tools of nonlinear dy namics can be irreplaceable for revealing hidden mechanisms subserving, for example, neuronal synchronization and periodic oscillations. The benefits for the brain of adopting chaotic regimes with their wide range of potentia l behaviours and their aptitude to quickly react to changing conditions wil l also be considered. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.