Pattern formation in a ratio-dependent predator-prey model with cross diffusion

Qing Li; Junfeng He; Qing Li; Junfeng He

doi:10.3934/era.2023055

Electronic Research Archive

2023, Volume 31, Issue 2: 1106-1118. doi: 10.3934/era.2023055

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Pattern formation in a ratio-dependent predator-prey model with cross diffusion

Qing Li ¹,
Junfeng He ^{2
,
,}

1.
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
2.
College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China

Received: 25 August 2022 Revised: 21 November 2022 Accepted: 05 December 2022 Published: 15 December 2022

This paper is focused on a ratio-dependent predator-prey model with cross-diffusion of quasilinear fractional type. By applying the theory of local bifurcation, it can be proved that there exists a positive non-constant steady state emanating from its semi-trivial solution of this problem. Further based on the spectral analysis, such bifurcating steady state is shown to be asymptotically stable when the cross diffusion rate is near some critical value. Finally, numerical simulations and ecological interpretations of our results are presented in the discussion section.
- cross-diffusion,
- predator-prey model,
- bifurcation,
- stability
Citation: Qing Li, Junfeng He. Pattern formation in a ratio-dependent predator-prey model with cross diffusion[J]. Electronic Research Archive, 2023, 31(2): 1106-1118. doi: 10.3934/era.2023055

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Abstract

This paper is focused on a ratio-dependent predator-prey model with cross-diffusion of quasilinear fractional type. By applying the theory of local bifurcation, it can be proved that there exists a positive non-constant steady state emanating from its semi-trivial solution of this problem. Further based on the spectral analysis, such bifurcating steady state is shown to be asymptotically stable when the cross diffusion rate is near some critical value. Finally, numerical simulations and ecological interpretations of our results are presented in the discussion section.

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