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Characterizing the effects of self- and cross-diffusion on stationary patterns of a predator–prey system
journal contribution
posted on 2023-06-09, 19:58 authored by Jai-Fang Zhang, Hong-Bo Shi, Anotida MadzvamuseAnotida MadzvamuseIn 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 ChaosISSN
0218-1274Publisher
World Scientific PublishingExternal DOI
Issue
3Volume
30Page range
1-20Article number
a2050041Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-12-17First Open Access (FOA) Date
2021-03-16First Compliant Deposit (FCD) Date
2019-12-16Usage metrics
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