Dynamics of bound states of same-chirality spiral waves

Christian W. Zemlin, Karthik Mukund, Vadim N. Biktashev, Arkady M. Pertsov

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Abstract

We describe the dynamics of bound states of same-chirality spirals in a generic numerical model of an excitable medium. For each bound state, we analyze its tip trajectory patterns and determine its characteristic frequencies. We report two previously unidentified bound states: for spiral pairs, a state that exhibits alternating cycles of small and large distances between collisions (A2); for triplets, the first example of a meandering bound state (M3). In parameter space, A2 lies in between the previously described oscillating pairs (O2) and master-slave pairs (MS). We present numerical evidence that the transition O2 ↠A2 occurs via a supercritical period-doubling bifurcation, while the transition A2 ↠MS occurs via a symmetry breaking secondary Hopf bifurcation. A classification of all regimes according to dynamical systems theory exposes the wealth of phenomena exhibited by multiarmed spiral waves.

Original languageEnglish
Article number016207
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number1
DOIs
StatePublished - 2006

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