论文标题
耦合杂斜周期的混乱及其分段代表
Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation
论文作者
论文摘要
我们考虑两个稳定的杂斜循环，这些循环沿相反的方向旋转，并通过扩散术语耦合。该系统中的完整同步是不可能的，数值探索表明，在低水平的耦合下，混乱很丰富。随着耦合强度的提高，观察到了几种变化对称性的转变，最后通过倍增的级联反向出现稳定的周期性轨道。为了在极小的耦合处揭示行为，建议了动力学的分段构模型。在此模型中，我们在数字上为混乱状态构造了一个庞加莱的图，它似乎是一个不可糊化的圆形图，因此在小耦合极限中确认了大量混乱。我们还表明，在分段恒定描述中，由于耦合中的死区域，在子系统之间有一组周期性解决方案。
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of coupling. With increase of coupling strength, several symmetry-changing transitions are observed, and finally a stable periodic orbit appears via an inverse period-doubling cascade. To reveal the behavior at extremely small couplings, a piecewise-constant model for the dynamics is suggested. Within this model we construct a Poincaré map for a chaotic state numerically, it appears to be an expanding non-invertable circle map thus confirming abundance of chaos in the small coupling limit. We also show that within the piecewise-constant description, there is a set of periodic solutions with different phase shifts between subsystems, due to dead zones in the coupling.
