Input-to-State Stability for Impulsive Gilpin-Ayala Competition Model With Reaction Diffusion and Delayed Feedback

Abstract

This study focuses on the input-to-state stability issue for impulsive Gilpin-Ayala competition model with reaction diffusion and delayed feedback. By using a fixed point theorem, variational method and Lyapunov function method, the unique existence of globally asymptotical input-to-state stability of positive stationary solution is established under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of Reaction-Diffusion (RD) Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. In the end, simulation results are presented to validate the effectiveness and feasibility of the proposed results.

Keywords

• Gilpin-Ayala competition model
• globally asymptotical stability
• Lyapunov function
• Markovian jumping