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Analysis on existence of bifurcation solutions for a predator-prey model with herd behavior. (English) Zbl 07166434
Summary: This paper is concerned with a diffusive predator-prey model with herd behavior. The local and global stability of the unique homogeneous positive steady state \(U^*\) is obtained. Treating the conversion or consumption rate \(\gamma\) as the bifurcation parameter, the steady-state bifurcations both from simple and double eigenvalues are studied near \(U^*\). The techniques include the Lyapunov function, the spectrum analysis of operators, the bifurcation theory, space decompositions and the implicit function theorem.

35 Partial differential equations
34 Ordinary differential equations
Full Text: DOI
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