Enhanced Resonance by Coupling and Summing in Sinusoidally Driven Chaotic Neural Networks

Shin MIZUTANI  Takuya SANO  Katsunori SHIMOHARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.4   pp.648-657
Publication Date: 1999/04/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
driven chaotic system,  chaotic neural network,  biological information processing,  stochastic resonance,  enhancement,  coupling,  

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Summary: 
Enhancement of resonance is shown by coupling and summing in sinusoidally driven chaotic neural networks. This resonance phenomenon has a peak at a drive frequency similar to noise-induced stochastic resonance (SR), however, the mechanism is different from noise-induced SR. We numerically study the properties of resonance in chaotic neural networks in the turbulent phase with summing and homogeneous coupling, with particular consideration of enhancement of the signal-to-noise ratio (SNR) by coupling and summing. Summing networks can enhance the SNR of a mean field based on the law of large numbers. Global coupling can enhance the SNR of a mean field and a neuron in the network. However, enhancement is not guaranteed and depends on the parameters. A combination of coupling and summing enhances the SNR, but summing to provide a mean field is more effective than coupling on a neuron level to promote the SNR. The global coupling network has a negative correlation between the SNR of the mean field and the Kolmogorov-Sinai (KS) entropy, and between the SNR of a neuron in the network and the KS entropy. This negative correlation is similar to the results of the driven single neuron model. The SNR is saturated as an increase in the drive amplitude, and further increases change the state into a nonchaotic one. The SNR is enhanced around a few frequencies and the dependence on frequency is clearer and smoother than the results of the driven single neuron model. Such dependence on the drive amplitude and frequency exhibits similarities to the results of the driven single neuron model. The nearest neighbor coupling network with a periodic or free boundary can also enhance the SNR of a neuron depending on the parameters. The network also has a negative correlation between the SNR of a neuron and the KS entropy whenever the boundary is periodic or free. The network with a free boundary does not have a significant effect on the SNR from both edges of the free boundaries.