Dynamics Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Smith Growth Rate and B-D Functional Response
This paper mainly studies the stability analysis of a class of delayed reaction-diffusion predator-prey systems with Smith growth rate and B-D functional response function.Firstly,we calculate the existence and stability conditions of equilibrium for the ordinary differential system,and provide corresponding numerical simulation results.Secondly,we use Taylor expansion to transform the delayed reaction-diffusion system into a reaction-diffusion system,and obtain the parameter space where the system undergoes Turing bifurcation at the positive equilibrium through eigenvalue analysis.Finally,we provide numerical simulations of the system undergoing Turing bifurcation,and analyze the effects of delay parameter r and cross-diffusion coefficient on the dynamical behavior of the system.These theoretical results will provide important help for understanding the regulatory relationship between populations.
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