Mathematical description of brain dynamics in perception and action

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Abstract:

A given but otherwise random environmental time series impinging on the input of a certain biological processor passes through with overwhelming probability practically undetected. A very small percentage of environmental stimuli, though, is ‘captured’ by the processor's nonlinear dissipative operator as initial conditions, and is ‘processed’ as solutions of its dynamics. The processor, then, is in such cases instrumental in compressing or abstracting those stimuli, thereby making the external world to collapse from a previous regime of a ‘pure state’ of suspended animation into a set of stable complementary and mutually exclusive eigenfunctions or ‘categories'. The characteristics of this cognitive set depend on the operator involved and the hierarchical level where the abstraction takes place. Depending on the context, the transition from one state to another occurs in such a cognitive operator. The chaotic itinerancy may play a crucial role for this process. In this paper we model the dynamics which may underlie such a cognitive process and the role of the thalamo-cortical pacemaker of the (human) brain. In order to model them, conceptualization by the notion of ‘attractor ruin’ in high-dimensional dynamical systems is necessary.

Document Type: Research Article

Affiliations: 1: Department of Electrical Engineering, University of Patras, Greece. 2: Email: tsuda@math.sci.hokudai.ac.jp

Publication date: January 1, 1999

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