Some aspects of nonlocal dynamics on directed and undirected networks for an initial value problem whose Jacobian matrix is a variable-order fractional power of a Laplacian matrix are discussed here. Both directed and undirected graphs are considered. Under appropriate assumptions, the existence, uniqueness, and uniform asymptotic stability of the solutions of the underlying initial value problem are proved. Some examples giving a sample of the behavior of the dynamics are also included.

翻译：此处讨论在定向和非定向网络上用于初始价值问题的非本地动态的某些方面,即Jacobian矩阵是拉普拉西亚矩阵的可变顺序分数能力,其中既考虑定向图,也考虑非定向图。在适当的假设下,可以证明原始价值问题解决方案的存在、独特性和统一性。还列举了一些实例,举例说明了动态行为。