Pattern Formation in a Predator-Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Abstract

With the rapid development of network science, Turing pattern on complex networks has attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator-prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing pattern is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing pattern. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing pattern is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing pattern, which is not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing pattern and spatiotemporal pattern. We believe that these findings contribute to a better understanding of self-organization on complex networks.