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

Lei Shi, Jiaying Zhou and Yong Ye ()
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Lei Shi: School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
Jiaying Zhou: School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Yong Ye: School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China

Mathematics, 2023, vol. 11, issue 15, 1-15

Abstract: With the rapid development of network science, Turing patterns on complex networks have 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 patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. 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 patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks.

Keywords: Turing pattern; predator–prey model; multiplex networks; spatiotemporal pattern (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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