Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

Abstract

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.