Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 54, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2020.103106
Keywords
Predator-prey model; Hunting cooperation; Cross-diffusion; Turing bifurcation; Pattern
Categories
Funding
- Natural Science Foundation of Zhejiang Province of China [LY19A010010]
- National Natural Science Foundation of China [11971143]
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This paper presents a qualitative study of a diffusive predator-prey system with the hunting cooperation functional response. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium are explicitly determined. It is shown that the hunting cooperation affects not only the existence of the positive equilibrium but also the stability. For the diffusive system, the stability and cross-diffusion driven Turing instability are investigated according to the relationship of the self-diffusion and the cross-diffusion coefficients. Stability and cross-diffusion instability regions are theoretically determined in the plane of the cross-diffusion coefficients. The technique of multiple time scale is employed to deduce the amplitude equation of Turing bifurcation and then pattern dynamics driven by the cross-diffusion is also investigated by the corresponding amplitude equation. (C) 2020 Elsevier Ltd. All rights reserved.
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