Dynamics analysis of a delayed reaction-diffusion predator-prey system with non-continuous threshold harvesting

This paper deals with a delayed reaction-diffusion predator-prey model with non-continuous threshold harvesting. Sufficient conditions for the local stability of the regular equilibrium, the existence of Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation. By utilizing upper-lower solution method and Lyapunov functions the globally asymptotically stability of a unique regular equilibrium and asymptotically stability of a unique pseudoequilibrium are studied respectively. Further, the boundary node bifurcations are studied. Finally, numerical simulation results are presented to validate the theoretical analysis.