Kim S Y, Lim W
Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Feb;63(2 Pt 2):026217. doi: 10.1103/PhysRevE.63.026217. Epub 2001 Jan 25.
We investigate the loss of chaos synchronization in coupled chaotic systems without symmetry from the point of view of bifurcations of unstable periodic orbits embedded in the synchronous chaotic attractor (SCA). A mechanism for direct transition to global riddling through a transcritical contact bifurcation between a periodic saddle embedded in the SCA and a repeller on the boundary of its basin of attraction is thus found. Note that this bifurcation mechanism is different from that in coupled chaotic systems with symmetry. After such a riddling transition, the basin becomes globally riddled with a dense set of repelling tongues leading to divergent orbits. This riddled basin is also characterized by divergence and uncertainty exponents, and thus typical power-law scaling is found.
我们从嵌入同步混沌吸引子（SCA）的不稳定周期轨道的分岔角度，研究了非对称耦合混沌系统中混沌同步的丧失。由此发现了一种通过SCA中嵌入的周期鞍点与吸引域边界上的排斥子之间的跨临界接触分岔直接过渡到全局 riddling 的机制。请注意，这种分岔机制与具有对称性的耦合混沌系统中的不同。经过这样的 riddling 转变后，吸引域会因密集的排斥舌集而全局 riddled，导致轨道发散。这个 riddled 吸引域还具有发散和不确定性指数的特征，因此发现了典型的幂律标度。
