Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems

Abstract

Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among "exotic" attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

The golden mean as clock cycle of brain waves

“…El Naschie [58,60,61] and others developed for the fundamental question of time reversibility the notion of a Cantorian space-time (compare the idea of Cantor coding by Tsuda [59]). What is really remarkable of this Cantorian space-time is that applying all the probabilistic necessary laws, the values of the Hausdorff dimension are intrinsically linked to the golden mean and its successive powers.…”

Chaotic itinerancy and its roles in cognitive neurodynamics

“…Among others, we proposed a neural chaotic itinerancy [1,2,3,4,5], where typical cortical transitions are not merely random but are transitory and chaotic dynamics (see, for example, [6]). …”

Dynamics of human neocortex that optimizes its stability and flexibility

“…Evidence for brain stability comes from demonstrations that reproducible patterns recur in reproducible behavioral states [Freeman, 2005]. Computational evidence for flexibility and stability comes from a hierarchy of models of nonlinear brain dynamics called K-sets [Freeman, 1975[Freeman, , 2000Kozma and Freeman, 2001;Principe et al, 2001;Kozma, Freeman and Erdí, 2003], which are related to the models of Friston [2000], Tsuda [2001], and Stam et al [2003], and which serve to simulate multiple states of unit and field potentials and their changes with learning. The multiplicity of states shows that brains are intrinsically unstable in jumping from each state to the next by state transitions, which closely resemble phase transitions in physical media [Haken, 1983].…”