학술논문
Synchronization of Turing patterns in complex networks of reaction-diffusion systems set in distinct domains.
Document Type
Journal
Author
Aziz-Alaoui, M. A. (F-NORMU-MAH) AMS Author Profile; Cantin, Guillaume (F-NANT-S2N) AMS Author Profile; Thorel, Alexandre (F-NORMU-MAH) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35B Qualitative properties of solutions
35B36Pattern formation
35B40Asymptotic behavior of solutions
35Partial differential equations -- 35R Miscellaneous topics
35R02Partial differential equations on graphs and networks
92Biology and other natural sciences -- 92C Physiological, cellular and medical topics
92C17Cell movement
35B36
35B40
35
35R02
92
92C17
Language
English
Abstract
Summary: ``We present an innovative complex network of reaction-diffusion systems set in distinct domains, with boundary couplings. The complex network models the evolution of interacting populations living in a heterogeneous and fragmented habitat, whose biological individuals migrate from one patch to another. In our model, the displacements of individuals are described by mixed boundary couplings, involving both the Neumann and Robin boundary conditions, which improve the modeling of migrations by point-wise couplings. We investigate the cases of diffusion in isotropic and anisotropic habitats and establish original sufficient conditions of synchronization in this complex network model, for complete graphs, cyclic graphs and rings of nearest neighbors. In parallel, we apply our theoretical framework to a nonlinear predator-prey model with Leslie-Gower-type functional response and explore numerically the emergence of synchronization on heterogeneous Turing patterns.''