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

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.

Automated summary

Predator-prey models have attracted attention in various disciplines and the theory of pattern formation in monolayer networks has been extensively studied. This study extends the theory to multiplex networks, which are common in diverse areas. Furthermore, the model is enhanced with cross-diffusion to account for specific movement tendencies of each species. The linear analysis reveals the theoretical Turing instability region and demonstrates that either the multiplex network topology or cross-diffusion can destabilize the homogeneous fixed point, resulting in various Turing patterns. The experimental simulation results confirm the validity of the theoretical analysis.