允许持久同步的耦合函数的一般理论
Towards a general theory for coupling functions allowing persistent synchronization
摘要：
研究了具有类似扩散作用的耦合动力系统网络的同步性质。我们假设孤立节点动力学具有一个向前不变集，在该不变集上有一个有界雅可比矩阵，然后我们构造了一类耦合函数，它允许在连接的复杂网络中实现一致稳定的同步-在这个意义上，有一个开放的初始条件的邻域，它被一致地吸引向同步。此外，这种稳定的同步持续扰动下不相同的节点动态。我们用数值例子说明了理论，并得出结论，讨论嵌入这些结果在一个更一般的框架谱二分法。
英文摘要：
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we characterise a class of coupling functions that allows for uniformly stable synchronisation in connected complex networks --- in the sense that there is an open neighbourhood of the initial conditions that is uniformly attracted towards synchronisation. Moreover, this stable synchronisation persists under perturbations to non-identical node dynamics. We illustrate the theory with numerical examples and conclude with a discussion on embedding these results in a more general framework of spectral dichotomies.
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