Mathematical Biosciences and Engineering (MBE)

On a diffusive predator-prey model with nonlinear harvesting

Pages: 807 - 821, Volume 11, Issue 4, August 2014      doi:10.3934/mbe.2014.11.807

       Abstract        References        Full Text (953.2K)       Related Articles       

Peng Feng - Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965, United States (email)

Abstract: In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

Keywords:  Predator-prey, Leslie-Gower, nonlinear harvesting, turing instability, pattern formation, global stability.
Mathematics Subject Classification:  Primary: 35K40, 35K57, 35B36; Secondary: 35Q92.

Received: August 2013;      Accepted: November 2013;      Available Online: March 2014.