Nonlinear control ecological model with complex discrete map

In this paper, a predation model with nonlinear state feedback control is proposed and discussed. The properties of the Poincare map defined on the phase set and the dynamic properties of the impulsive dynamic system are discussed. First, the precise pulse set and phase set of the Poincare map are discussed in detail in various situations. Then, the Poincare map is determined and its analytical properties are studied. Secondly, the nec-essary and sufficient conditions for the global stability of the order-1 periodic solution of the impulsive semi-dynamic system are studied. Finally, numerical simulations verify the correctness of the theoretical results. The results show that under our nonlinear state feedback control, the density of prey will keep changing periodically, thus being effectively controlled. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes and discusses a predation model with nonlinear state feedback control. The properties of the Poincare map defined on the phase set and the dynamic properties of the impulsive dynamic system are investigated. The precise pulse set and phase set of the Poincare map are discussed in various situations, and the analytical properties of the Poincare map are studied. The necessary and sufficient conditions for the global stability of the order-1 periodic solution of the impulsive semi-dynamic system are also examined.