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Bifurcation in asymmetrically coupled BVP oscillators. (English) Zbl 1064.34513

Summary: BVP oscillator is the simplest mathematical model describing dynamical behavior of neural activity. Large-scale neural network can often be described naturally by coupled systems of BVP oscillators. However, even if two BVP oscillators are merely coupled by a linear element, the whole system exhibits complicated behavior. We analyze coupled BVP oscillators with asymmetrical coupling structure, besides, each oscillator has different internal resistance. The system shows a rich variety of bifurcation phenomena and strange attractors. We calculate bifurcation diagrams in two-parameter plane around which the chaotic attractors mainly appear and confirm relaxant phenomena in the laboratory experiments. We also briefly report a conspicuous strange attractor.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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References:

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