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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.

##### MSC:
 35 Partial differential equations 34 Ordinary differential equations
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##### References:
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