Analysis on existence of bifurcation solutions for a predator-prey model with herd behavior. (English) Zbl 1480.92183
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:
| 92D25 | Population dynamics (general) |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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