TY - JOUR

T1 - Dynamics of bound states of same-chirality spiral waves

AU - Zemlin, Christian W.

AU - Mukund, Karthik

AU - Biktashev, Vadim N.

AU - Pertsov, Arkady M.

PY - 2006

Y1 - 2006

N2 - 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 â† A2 occurs via a supercritical period-doubling bifurcation, while the transition A2 â† 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.

AB - 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 â† A2 occurs via a supercritical period-doubling bifurcation, while the transition A2 â† 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.

UR - http://www.scopus.com/inward/record.url?scp=33746253313&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.74.016207

DO - 10.1103/PhysRevE.74.016207

M3 - Article

C2 - 16907177

AN - SCOPUS:33746253313

SN - 1539-3755

VL - 74

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 1

M1 - 016207

ER -