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Characterizing the effects of self- and cross-diffusion on stationary patterns of a predator–prey system

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posted on 2023-06-09, 19:58 authored by Jai-Fang Zhang, Hong-Bo Shi, Anotida MadzvamuseAnotida Madzvamuse
In this paper, we study a nonlinear coupled predator–prey diffusion system which widely exists in ecosystem. It is found that the self-diffusion and cross-diffusion do not change the stability of the semi-equilibrium point of the corresponding predator–prey system. However, the two kinds of diffusion play an important role on the positive equilibrium, in virtue of which Turing instability of the corresponding diffusion system either continues to exist or disappears and becomes stable. On the stationary patterns of the nonlinear coupled system, we find some interesting results which differ from the phenomenon found in corresponding diffusion system. Strong cross-diffusion can make the corresponding system generate stationary patterns. Finally, numerical simulation is also done to verify the existence of the effects of self-diffusion and cross-diffusion.

Funding

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149

New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017

InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION

History

Publication status

  • Published

File Version

  • Accepted version

Journal

International Journal of Bifurcation and Chaos

ISSN

0218-1274

Publisher

World Scientific Publishing

Issue

3

Volume

30

Page range

1-20

Article number

a2050041

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-12-17

First Open Access (FOA) Date

2021-03-16

First Compliant Deposit (FCD) Date

2019-12-16

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