Bifurcation analysis of a predator-prey system with self- and cross-diffusion and constant harvesting rate | Zendy

Hunki Baek | Zendy

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Bifurcation analysis of a predator-prey system with self- and cross-diffusion and constant harvesting rate

Author(s) -

Hunki Baek

Publication year - 2014

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2014.1.29

Subject(s) - mathematics , constant (computer programming) , bifurcation , hopf bifurcation , stability (learning theory) , pattern formation , mathematical analysis , focus (optics) , diffusion , domain (mathematical analysis) , turing , statistical physics , computer science , physics , nonlinear system , machine learning , optics , genetics , programming language , thermodynamics , quantum mechanics , biology

In this paper, we focus on a ratio dependent predator-prey system with self- and cross-diffusion and constant harvesting rate. By making use of a brief stability and bifurcation analysis, we derive the symbolic conditions for Hopf, Turing and wave bi- furcations of the system in a spatial domain. Additionally, we illustrate spatial pattern formations caused by these bifurcations via numerical examples. A series of numerical examples reveal that one can observe several typical spatiotemporal patterns such as spotted, spot-stripelike mixtures due to Turing bifurcation and an oscillatory wave pat- tern due to the wave bifurcation. Thus the obtained results disclose that the spatially extended system with self-and cross-diffusion and constant harvesting rate plays an important role in the spatiotemporal pattern formations in the two dimensional space.

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