Name
Title | ||
|---|---|---|
Fold-Pitchfork Bifurcation, Arnold Tongues And Multiple Chaotic Attractors In A Minimal Network Of Three Sigmoidal Neurons |
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1142/S0218127418501237 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS |
Keywords | Field | DocType |
Chaotic neural network, fold-pitchfork bifurcation, Arnold tongue, crisis | Attractor,Mathematical analysis,Arnold tongue,Chaotic,Pitchfork bifurcation,Chaotic neural network,Mathematics,Sigmoid function | Journal |
Volume | Issue | ISSN |
28 | 10 | 0218-1274 |
Citations | PageRank | References |
1 | 0.35 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yo Horikawa | 1 | 50 | 11.88 |
| Hiroyuki Kitajima | 2 | 49 | 9.35 |
| Haruna Matsushita | 3 | 33 | 8.98 |