This paper considers the synchronization of a class of delayed and nonlinearly coupled complex networks that are subject to discontinuous dynamics and exogenous disturbances. One distinguishing feature of this class of complex networks is the non-continuous nature of their node dynamics so that the usual Lipschitz and other relative conditions are not satisfied and that the existence of continuously differentiable solutions is not guaranteed. Both nondelayed and delayed networks in this class are considered. Some sufficient criteria of synchronization are obtained under a new controller using the Lyapunov stability theory of nonsmooth dynamical systems. Two numerical simulations are given to illustrate our main theoretical findings.

中文翻译：

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具有不连续动态和外源干扰的复杂动态网络的同步

本文考虑了一类受不连续动力学和外源干扰影响的延迟非线性耦合复杂网络的同步问题。这类复杂网络的一个显着特征是其节点动态的非连续性，因此不满足通常的 Lipschitz 和其他相关条件，并且不能保证连续可微解的存在。考虑了此类中的非延迟和延迟网络。利用非光滑动力系统的李雅普诺夫稳定性理论，在新控制器下获得了一些充分的同步准则。给出了两个数值模拟来说明我们的主要理论发现。