Synchronizing Moore and Spiegel

This paper presents a study of bifurcations and synchronization (in the sense of Pecora and Carroll [Phys. Rev. Lett. {\bf 64}, 821-824 (1990)]) in the Moore-Spiegel oscillator equations. Complicated patterns of period-doubling, saddle-node and homoclinic bifurcations are found and analysed. 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.

Co-authored with Dr N.J. Balmforth.

Chaos, 7, 738-752, 1997

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