STABILITY OF A NONAUTONOMOUS DELAYED PERIODIC REACTION-DIFFUSION PREDATOR-PREY MODEL

This article focuses on the stability of periodic solution of a delayed nonautonomous reaction-diffusion predator-prey model. The fine combination of upper and lower solution methods and Lyapunov stability theory is used to transform the study of the stability problem of delayed reaction-diffusion equations into the stability problem of their corresponding delayed ordinary differential equations. Some sufficient conditions are given to ensure the globally asymptotically stability of the periodic solution for this model. Unlike existing results, the stable solution which are obtained in this article is a time-periodic solution rather than a constant periodic solution or a solution for a steady-state system. We extend a stability theorem on predator-prey model introduced by V. Ortega and C. Rebelo in 2023 to nonautonomous delayed reaction-diffusion model. Finally, in order to show the application of the theoretical results, the proposed conditions are numerically validated over a 2-periodic delayed nonautonomous reaction-diffusion predator-prey model.