TY - JOUR
T1 - Riddling bifurcation in chaotic dynamical systems
AU - Lai, Ying Cheng
AU - Grebogi, Celso
AU - Yorke, James A.
AU - Venkataramani, S. C.
PY - 1996
Y1 - 1996
N2 - When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.
AB - When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.
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U2 - 10.1103/PhysRevLett.77.55
DO - 10.1103/PhysRevLett.77.55
M3 - Article
AN - SCOPUS:0001836881
SN - 0031-9007
VL - 77
SP - 55
EP - 58
JO - Physical review letters
JF - Physical review letters
IS - 1
ER -