Stability and cross-diffusion-driven instability in a diffusive predator–prey system with hunting cooperation functional response

• Published in: Nonlinear analysis: real world applications Vol. 54; p. 103106
• Main Authors: Song, Danxia, Li, Chao, Song, Yongli
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.08.2020; Elsevier BV
• Subjects: Amplitudes; Cooperation; Cross-diffusion; Hopf bifurcation; Hunting; Hunting cooperation; Pattern; Predator–prey model; Self diffusion; Stability; Turing bifurcation; Pattern; Cross-diffusion; Hunting cooperation; Predator–prey model; Turing bifurcation
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2020.103106

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.