Journal ArticleDOI
Chaos, torus and synchronization from three coupled relaxation oscillators
Toshimichi Saito,Y. Matsumoto +1 more
TLDR
In this paper, fundamental phenomena from three coupled relaxation oscillators are analyzed and a rough bifurcation diagram is given, indicating that 3-torus is popular for weak coupling and chaos is more popular for relatively strong coupling.Abstract:
This paper analyzes fundamental phenomena from three coupled relaxation oscillators. The system nonlinearity is a piecewise linear hysteresis comparator and we can explicitly calculate the return map and its Lyapunov exponents. Then we clarify generation of chaos, 2-torus, 3-torus and various kinds of synchronizations. Also, a rough bifurcation diagram is given. It indicates that 3-torus is popular for weak coupling and chaos is popular for relatively strong coupling. Some of the phenomena are confirmed by laboratory measurements. >read more
Citations
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Analysis of bifurcation phenomena in a 3-cells hysteresis neural network
TL;DR: In this paper, a simplified hysteresis neural network with three cells and three control parameters is considered and the return map and Lyapunov exponents are calculated by using the piecewise exact solution.
Journal ArticleDOI
Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes
TL;DR: In this article, the authors investigated the mechanism of chaos via torus breakdown observed in a simple four-dimensional autonomous circuit including two diodes and derived the Poincare mapping.
Journal ArticleDOI
Novel bifurcation structure generated in piecewise-linear three-LC resonant circuit and its Lyapunov analysis
TL;DR: In this paper, a piecewise-linear oscillator consisting of a three-L C resonant circuit with a hysteresis element is analyzed, and a detailed bifurcation diagram is obtained, where two-torus generating regions exist in a 3-LC generating region.
Journal ArticleDOI
Bifurcation scenarios for a 3D torus and torus-doubling
Naohikio Inaba,Munehisa Sekikawa,Yoshimasa Shinotsuka,Kyohei Kamiyama,Ken'ichi Fujimoto,Tetsuya Yoshinaga,Tetsuro Endo +6 more
TL;DR: Bifurcation scenarios for a 3D torus and torus-doubling Naohikio Inaba1,∗, Munehisa Sekikawa2, Yoshimasa Shinotsuka3, Kyohei Kamiyama3, Ken’ichi Fujimoto4, Tetsuya Yoshinaga4, and Tetsuro Endo3 as discussed by the authors.
Journal ArticleDOI
Three-torus-causing mechanism in a third-order forced oscillator
TL;DR: The three-torus-causing mechanism in a third-order forced oscillator was investigated in this paper, where it was shown that the mechanism can cause the three torus causing mechanism in the forced oscillators.
References
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The dimension of chaotic attractors
TL;DR: In this paper, the authors discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors, and conclude that dimension of the natural measure is more important than the fractal dimension.
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Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos
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Synchronization of chaos
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Attractors on an N-torus: Quasiperiodicity versus chaos
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Journal ArticleDOI
Three-frequency quasiperiodicity, phase locking, and the onset of chaos
P. S. Linsay,A. W. Cumming +1 more
TL;DR: In this article, the authors performed a series of experiments with coupled relaxation oscillators to study three-frequency quasiperiodicity and found strong evidence for the Ruelle-Takens scenario for the transition to chaos although only a small portion of parameter space is occupied by chaos.