The spatial patterns through diffusion-driven instability in a predator-prey model. (English) Zbl 1242.35207

Summary: Studies on stability mechanism and bifurcation analysis of a system of interacting populations by the combined effect of self and cross-diffusion become an important issue in ecology. In the current investigation, we derive the conditions for existence and stability properties of a predator-prey model under the influence of self and cross-diffusion. Numerical simulations have been carried out in order to show the significant role of self and cross-diffusion coefficients and other important parameters of the system. Various contour pictures of spatial patterns through Turing instability are portrayed and analysed in order to substantiate the applicability of the present model. Finally, the paper ends with an extended discussion of biological implications of our findings.


35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K45 Initial value problems for second-order parabolic systems
92D25 Population dynamics (general)
35B32 Bifurcations in context of PDEs
35K57 Reaction-diffusion equations
Full Text: DOI


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