Dynamics of a predator-prey model with nonlinear growth rate and B-D functional response?

In this paper, a predator-prey diffusive model, subject to homogeneous Dirichlet boundary conditions, with Beddington-DeAngelis functional response and nonlin-ear growth rate on the predator is proposed and the well posedness of its solution is systematically studied. Taking the capture rate m as the main parameter, we mainly investigate the existence, stability and exact number of positive solutions when m is large and other parameters meet a certain range of conditions. Meanwhile, some numerical simulations are applied to illustrate the analytical results. The main techniques used in this paper include the fixed point index theory, the super-sub solution method, the Lyapunov-Schmidt reduction procedure and the perturbation principle.(c) 2022 Elsevier Ltd. All rights reserved.