Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

Abstract

Abstract In this paper, we establish a unilateral diffusion Gompertz model of a single population in two patches in a theoretical way. Firstly, we prove the existence and uniqueness of an order-one periodic solution by the geometry theory of differential equations and the method of successor function. Secondly, we prove the stability of the order-one periodic solution by imitating the theory of the limit cycle of an ordinary differential equation. Finally, we verify the theoretical results by numerical simulations.

Keywords

• unilateral diffusion
• order-one periodic solution
• limit cycle
• Gompertz model