具有时变耦合的离散动态网络的同步
Synchronization of discrete-time dynamical networks with time-varying couplings
摘要：
研究了具有时变耦合的离散动力网络的局部完全同步问题。我们对耦合随时间变化的条件是相当普遍的，包括网络结构和反应动力学的变化;例如，反应可以由随机动力系统驱动。一个基本工具是Hajnal直径的概念，我们推广到无限雅可比矩阵序列。Hajnal直径可以用来验证同步，我们表明，它是等价于其他数量已扩展到随时间变化的情况下，如投影半径，投影李雅普诺夫指数，和横向李雅普诺夫指数。此外，这些结果被用来调查的同步问题，耦合映射网络的时变拓扑结构和可能的定向和加权的边缘。在这种情况下，无限耦合矩阵的Hajnal直径可以用来衡量网络过程的同步性。我们证明了网络能够同步某些混沌映射当且仅当存在一个整数T>0，使得对于任意长度为T的时间间隔，存在一个顶点，该顶点可以通过该时间间隔内的有向路径访问其他顶点。
英文摘要：
We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include both variations in the network structure and in the reaction dynamics; the reactions could, for example, be driven by a random dynamical system. A basic tool is the concept of Hajnal diameter which we extend to infinite Jacobian matrix sequences. The Hajnal diameter can be used to verify synchronization and we show that it is equivalent to other quantities which have been extended to time-varying cases, such as the projection radius, projection Lyapunov exponents, and transverse Lyapunov exponents. Furthermore, these results are used to investigate the synchronization problem in coupled map networks with time-varying topologies and possibly directed and weighted edges. In this case, the Hajnal diameter of the infinite coupling matrices can be used to measure the synchronizability of the network process. As we show, the network is capable of synchronizing some chaotic map if and only if there exists an integer T>0 such that for any time interval of length T, there exists a vertex which can access other vertices by directed paths in that time interval.
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