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

• Main Author: Hunki Baek
• Format: Article
• Language: English
• Published: University of Szeged 2014-06-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: spatiotemporal pattern formation; a predator-prey system; constant harvesting; diffusion-reaction; turing patterns.
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=2932

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 bifurcations 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 pattern 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.