Ali Fathei, Menzinger Michael
Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Chaos. 1999 Jun;9(2):348-356. doi: 10.1063/1.166412.
Orbital stability of limit cycles is the result of the competing local tendencies of perturbations from the cycle to decay (during phases of local stability) and to grow (during phases of local instability), averaged over a cycle. We examine this coexistence of attractive and repulsive phases on limit cycles, including the local rates of expansion and contraction of phase space volumes. This is done in a frame of reference that moves along the orbit, to partially decouple motions tangential and perpendicular to the cycle. Dynamical systems used for illustration are the generalized Bonhoeffer-van-der-Pol and Rossler models, both far from and near to different types of bifurcations. Finally, it is shown that the nonuniformity of local stability in phase space affects the response of limit cycle oscillators to perturbations and gives rise to their phase-dependent response. (c) 1999 American Institute of Physics.
极限环的轨道稳定性是由围绕一个周期平均后的、来自极限环的扰动的两种相互竞争的局部趋势导致的，即扰动在局部稳定阶段衰减，而在局部不稳定阶段增长。我们研究了极限环上吸引相和排斥相的这种共存情况，包括相空间体积的局部膨胀率和收缩率。这是在一个沿轨道移动的参考系中完成的，以便部分解耦与极限环相切和垂直的运动。用于说明的动力系统是广义的邦霍夫尔-范德波尔模型和罗斯勒模型，它们分别远离和接近不同类型的分岔点。最后，结果表明相空间中局部稳定性的不均匀性会影响极限环振荡器对扰动的响应，并导致其产生相位依赖响应。（c）1999美国物理研究所。
