Qualitative analysis of a Hölling‐Tanner predator‐prey model with mutual interference

Qualitative analysis of a Hölling‐Tanner predator‐prey model with mutual interference

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Article ID: iaor2013929
Volume: 219
Issue: 10
Start Page Number: 5283
End Page Number: 5289
Publication Date: Jan 2013
Journal: Applied Mathematics and Computation
Authors:
Keywords: population, predator-prey model, Lyapunov
Abstract:

A reaction‐diffusion system arising from the Hölling–Tanner predator–prey model is proposed and mutual interference among predators is considered. Conditions for the local and global asymptotical stability of equilibrium solutions are given by means of analyzing eigenvalue spectrum as well as Lyapunov functionals. Some non‐existence results of non‐constant positive steady‐state solutions are obtained. Also, the numerical simulation is given to verify the theoretical results.

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