Synchronizing Moore and Spiegel. (English) Zbl 0938.37018
Summary: This paper presents a study of bifurcations and synchronization, in the sense of L. M. Pecora and T. L. Carroll [Phys. Rev. Lett. 64, 821-824 (1990; Zbl 0938.37018)] in the Moore-Spiegel oscillator equations. Complicated patterns of period-doubling, saddle-node, and homoclinic bifurcations are found and analyzed. Synchronization is demonstrated by numerical experiment, periodic orbit expansion, and by using coordinate transformations. Synchronization via the resetting of a coordinate after a fixed interval is also successful in some cases. The Moore-Spiegel system is one of a general class of dynamical systems and synchronization is considered in this more general context.
MSC:
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
37C45 | Dimension theory of smooth dynamical systems |
94C05 | Analytic circuit theory |
37N35 | Dynamical systems in control |
Keywords:
complicated patterns; period-doubling; saddle-node; homoclinic bifurcations; synchronization; periodic orbit expansion; Moore-Spiegel oscillator; oscillatorCitations:
Zbl 0938.37018References:
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