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- Title
Grazing Bifurcations, Homoclinic Orbits and Chaos in a Ring Network of Linear Neuron-Like Elements with a Single Nonmonotonic Piecewise Constant Output Function.
- Authors
Horikawa, Yo
- 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.
- Subjects
RING networks; ORBITS (Astronomy); GRAZING
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2023, Vol 33, Issue 12, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127423501419