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 ↠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.
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 ↠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.
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 -