Symbolic dynamics of a chaotic neuron model

Abstract

Chaotic neurons change their internal state according to a bimodal map, and when they communicate with other neurons their internal state is transformed into one of two separate outputs, firing or resting. We address and investigate the topological entropy of the two-valued output of the chaotic neuron from two different viewpoints: the dependence upon the parameters of the neurons, and the relationship to their threshold. From the former viewpoint, we clarify the mechanism that changes the shift space corresponding to the time series of the neuronal output. From the latter viewpoint, we examine the effect of small fluctuations on the threshold of the chaotic neuron.Key words Chaotic neuron 9 Symbolic dynamics -Fator code 9 Parry measure Introduction A chaotic neuron model, which is a discrete-time model of a neuron with chaotic dynamics, has many interesting features, such as a chaotic response and a devil's staircase-like structure of the firing rate. 1 It has also been reported that a network constl-ucted with chaotic neurons can produce higher funcions such as dynamic associative memory and 2 pattern recognition. Moreover, a chaotic neuron model has recently been implemented using LSI hardware.In simple terms, a chaotic neuron model consists of two elements. These are a bimodal map, which drives the inter-