Stability of periodic solution for a novel delayed nonautonomous reaction-diffusion food chain systems with ratio-dependent

In this paper, a novel delayed nonautonomous 3-species reaction-diffusive food chain system with ratio-dependent is studied. First, by utilizing the fixed point theorem and comparison theorem of delayed differential equation, sufficient conditions for the existence of strictly positive spatially homogeneous periodic solutions (SHPS) in the new system are derived. Second, by combining the upper and lower solution method (UALSM) for delayed parabolic partial differential equations with Lyapunov stability theory, further sufficient conditions for the global asymptotic stability of the SHPS in the new system are established. Finally, numerical simulations are conducted to verify the correctness of the theoretical results.