Grazing Bifurcations, Homoclinic Orbits and Chaos in a Ring Network of Linear Neuron-Like Elements with a Single Nonmonotonic Piecewise Constant Output Function
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Published:2023-09-30
Issue:12
Volume:33
Page:
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ISSN:0218-1274
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Container-title:International Journal of Bifurcation and Chaos
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language:en
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Short-container-title:Int. J. Bifurcation Chaos
Affiliation:
1. Faculty of Engineering, Kagawa University, Takamatsu 761-0396, Japan
Abstract
The bifurcations and chaos of a ring of three unidirectionally coupled neuron-like elements are examined as a minimal chaotic neural network. The output function of one neuron is nonmonotonic and piecewise constant while those of the other two neurons are linear. Two kinds of nonmonotonic output functions are considered and it is shown that periodic solutions undergo grazing bifurcations owing to discontinuity in the nonmonotonic functions. Chaotic attractors are created directly through a grazing bifurcation and homoclinic orbits based at pseudo steady states are generated. It is shown that homoclinic/heteroclinic orbits satisfying the condition of Shil’nikov chaos are caused by overshoot in the nonmonotonic functions.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)