title: Dynamics of a diffusive predator-prey model with general nonlinear functional response.
abstract: We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.
authors.affiliation: School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China.
authors.forename: Wensheng
authors.identifier: 0000-0003-3131-9498
authors.initials: W
authors.lastname: Yang
mesh_terms: D000818:Animals; D008962:Models, Theoretical; D011235:Predatory Behavior