Nonlocal diffusion of variable order on complex networks. Issue 3 (3rd July 2022)

• Record Type: Journal Article
• Authors: Bertaccini, Daniele; Durastante, F.
• Is Part Of: International journal of computer mathematics. Volume 7:Issue 3(2022)
• Page Start: 172
• Page End: 191
• Publication Date: 2022-07-03
• Subjects: Network dynamics -- nonlocal dynamics -- superdiffusion; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2022.2114381
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : 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. This is a new extension to non-stationary behaviour of a class of non-local phenomena on complex networks for which 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 behaviour of the dynamics are also included.