A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay

Abstract

Abstract Allee effect (i.e. sparse effect) is active when the population density is small. Our purpose is to study such an effect of this phenomenon on population dynamics. We investigate an impulsive state feedback control single-population model with Allee effect and continuous delay. We first qualitatively analyze the singularity of this model. Then we obtain sufficient conditions for the existence of an order-one periodic orbit by the geometric theory of impulsive differential equations for the survival of endangered populations and obtain the uniqueness of an order-one periodic orbit by the monotonicity of the subsequent function. Furthermore, we prove the orbital asymptotic stability of an order-one periodic orbit using the geometric properties of successor functions to confirm the robustness of this control. Finally, we verify the correctness of our theoretical results by using some numerical simulations. Our results show that the release of artificial captive African wild dog (Lycaon pictus) can effectively protect the African wild dog population with Allee effect.

Keywords

• Qualitatively analysis
• Order-one periodic orbit
• Impulsive differential equation
• Allee effect