附加排斥力作用下耦合振子从振幅到振荡死亡的多种过渡途径
Diverse routes of transition from amplitude to oscillation death in coupled oscillators under additional repulsive link
摘要：
我们报道了在三个不同的扩散耦合系统中存在从振幅死亡（AD）到振荡死亡（OD）的不同过渡路径，这些系统被对称性破缺的排斥耦合链扰动。对于极限环系统的过渡是通过干草叉分叉（PB），如前所述，但在混沌系统中，它可以通过鞍结或跨临界分叉，这取决于单个系统的潜在动力学的性质。路线的多样性和它们对耦合系统的复杂动力学的依赖性不仅拓宽了我们对这一重要现象的理解，而且可能导致潜在的新的实际应用。
英文摘要：
We report the existence of diverse routes of transition from amplitude death (AD) to oscillation death (OD) in three different diffusively coupled systems, those are perturbed by a symmetry break- ing repulsive coupling link. For limit cycle systems the transition is through a pitchfork bifurcation (PB) as has been noted before, but in chaotic systems it can be through a saddle-node or a trans- critical bifurcation depending on the nature of the underlying dynamics of the individual systems. The diversity of the routes and their dependence on the complex dynamics of the coupled systems not only broadens our understanding of this important phenomenon but can lead to potentially new practical applications.
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