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Dynamic behaviors of a symmetrically coupled period-doubling system. (English) Zbl 1496.37046

Summary: A system of two coupled mappings demonstrates a variety of nonlinear phenomena such as the inverse state, spatiotemporal intermittence, traveling wave and the synchronization. In this paper, we are concerned with a system of symmetrically coupled quadratic mappings. B. P. Bezruchko et al. [Chaos Solitons Fractals 15, No. 4, 695–711 (2003; Zbl 1031.70012)] employed numerical method to study the bifurcation problem of such a system, but did not give a full investigation in theory because of the complicated computation. In this paper, we adopt the complete discrimination system theory and the real root isolation algorithm to overcome the difficulty. We will give a completed description of the bifurcations in theory for such a system, including the transcritical bifurcation, pitchfork bifurcation, flip bifurcation and the Neimark-Sacker bifurcation.

MSC:

37G10 Bifurcations of singular points in dynamical systems
37M20 Computational methods for bifurcation problems in dynamical systems
70K50 Bifurcations and instability for nonlinear problems in mechanics

Citations:

Zbl 1031.70012

Software:

DISCOVERER
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References:

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