On almost periodic processes in impulsive fractional-order competitive systems

Abstract

In this paper an impulsive model for the dynamics of competitive Lotka–Volterra systems using the Caputo fractional-order derivative is developed. The existence and uniqueness of almost periodic solutions are investigated. Applying the fractional Lyapunov method, we give sufficient conditions for global perfect uniform-asymptotic stability of the almost periodic solution and sufficient conditions to save these qualities at the uncertain case. Since the competitive relationship in ecosystem models is relevant in various contexts, including many population, neural nets or chemical kinetics problems, our results can be applied in the investigation of almost periodic processes in a wide range of competitive systems of diverse interest.