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- Title
Fold-Pitchfork Bifurcation, Arnold Tongues and Multiple Chaotic Attractors in a Minimal Network of Three Sigmoidal Neurons.
- Authors
Horikawa, Yo; Kitajima, Hiroyuki; Matsushita, Haruna
- Abstract
Bifurcations and chaos in a network of three identical sigmoidal neurons are examined. The network consists of a two-neuron oscillator of the Wilson–Cowan type and an additional third neuron, which has a simpler structure than chaotic neural networks in the previous studies. A codimension-two fold-pitchfork bifurcation connecting two periodic solutions exists, which is accompanied by the Neimark–Sacker bifurcation. A stable quasiperiodic solution is generated and Arnold's tongues emanate from the locus of the Neimark–Sacker bifurcation in a two-dimensional parameter space. The merging, splitting and crossing of the Arnold tongues are observed. Further, multiple chaotic attractors are generated through cascades of period-doubling bifurcations of periodic solutions in the Arnold tongues. The chaotic attractors grow and are destroyed through crises. Transient chaos and crisis-induced intermittency due to the crises are also observed. These quasiperiodic solutions and chaotic attractors are robust to small asymmetry in the output function of neurons.
- Subjects
BIFURCATION theory; CHAOS theory; ARTIFICIAL neural networks; PARAMETRONS; CELLULAR neural networks (Computer science); HOPF bifurcations
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2018, Vol 28, Issue 10, pN.PAG
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127418501237