On a diffusive predator-prey model with nonlinear harvesting
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.
Received: August 2013; Accepted: November 2013; Available Online: March 2014.
2015 5-year IF1.087