Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation

Meng Zhu, Jing Li and Xinze Lian ()
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Meng Zhu: College of Mathematics and Physics, Wenzhou University, Wenzhou 325000, China
Jing Li: School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou 325000, China
Xinze Lian: School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou 325000, China

Mathematics, 2022, vol. 10, issue 17, 1-20

Abstract: In this paper, we consider a Leslie–Gower cross diffusion predator–prey model with a strong Allee effect and hunting cooperation. We mainly investigate the effects of self diffusion and cross diffusion on the stability of the homogeneous state point and processes of pattern formation. Using eigenvalue theory and Routh–Hurwitz criterion, we analyze the local stability of positive equilibrium solutions. We give the conditions of Turing instability caused by self diffusion and cross diffusion in detail. In order to discuss the influence of self diffusion and cross diffusion, we choose self diffusion coefficient and cross diffusion coefficient as the main control parameters. Through a series of numerical simulations, rich Turing structures in the parameter space were obtained, including hole pattern, strip pattern and dot pattern. Furthermore, We illustrate the spatial pattern through numerical simulation. The results show that the dynamics of the model exhibits that the self diffusion and cross diffusion control not only form the growth of dots, stripes, and holes, but also self replicating spiral pattern growth. These results indicate that self diffusion and cross diffusion have important effects on the formation of spatial patterns.

Keywords: predator–prey; strong Allee effect; hunting cooperation; self diffusion; cross diffusion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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