Cross-diffusion induced Turing patterns on multiplex networks of a predator–prey model

Abstract

Predator–prey models have generated growing interest across disciplines ranging from mathematics to ecology. The theory of pattern formation in predator–prey systems organized in monolayer networks has often been investigated, due to its significance in both theoretical advances and practical applications. Here we broaden the theory to the case of multiplex networks, which are easily found in diverse areas, such as neuroscience, social networks, and transportation systems. Moreover, we incorporate the model with cross-diffusion by considering that each specie usually has a specific movement tendency. By carrying on the linear analysis, we get the theoretical Turing instability region and find that the homogeneous fixed point can become unstable due to either the topology of multiplex networks or the cross-diffusion, resulting in various Turing patterns. Furthermore, experimental simulation results are in great agreement with theoretical findings, verifying the theoretical analysis’ validity.