Dynamics of a diffusive predator-prey model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting. (English) Zbl 1336.35339
Summary: A diffusive predator-prey model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting subject to the homogeneous Neumann boundary condition is considered. We obtain the local and global stability of constant equilibria by eigenvalue analysis and iteration technique. Choosing some parameter concerning with harvesting as Hopf bifurcation parameter, we conclude the existence of periodic solutions near positive constant equilibrium. Using the normal form and center manifold theory, and numerical simulations, we demonstrate our theoretical results of stability and direction of periodic solutions. We also derive the non-existence and existence of non-constant positive steady states by energy method and degree theory.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35B32 | Bifurcations in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 92D25 | Population dynamics (general) |
Keywords:
Michaelis-Menten type prey harvesting; global stability; Hopf bifurcation; stationary pattern; degree theory; normal form; center manifoldReferences:
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