Periodic Solutions Of Three Kinds Of Population Dynamics Models With Impulsive Perturbations

Three kinds of population dynamics with impulsive disturbance are discussed in this paper,and the sparse effect is added to improve the applicability of the model.The dynamic properties of the model with impulsive perturbations at fixed time or state feedback are studied,especially the effect of impulsive effects on the periodic solutions of the system.Firstly,a predator-prey model with impulsive perturbation and sparse effect for Holling III type functional response is established.By applying a fixed-time impulse disturbance,the new model can be applied to the cases that the continuous models such as periodic pesticide spraying,periodic capture and periodic stocking cannot handle.By using the Mawhin's theory of coincidence degree and analysis tools,the existence of periodic solutions of the model is proved,and the sufficient conditions for the existence of periodic solutions are given,which are verified by numerical simulation.Then,the inte-grated control model of Coconut Leaf Beetle was studied.Coconut Leaf Beetle is one of the main pests of palm plants.Targeting at the characteristics of two kinds of parasitoids attacking coconut leaf beetles at different age Targeting at stages,this paper establishes the control model of periodic impulse spraying with different age structure and releas-ing natural enemies.The sufficient conditions for the existence of periodic solutions of the system and the corresponding numerical simulation results are obtained.The results show that the insect pest of Coconut Leaf Beetle can be effectively controlled under the condition of reasonable control of parasitic wasp dosage and spraying medicines.Finally,a class of Holling II predator-prey model with impulsive state feedback and strong Allee effect is established.Through the impulse effect of state feedback,the system is more in line with some practical conditions.The existence,uniqueness and stability of periodic solutions of semi-continuous dynamical systems under certain conditions are obtained by the successive function method based on the geometric theory of semi-continuous dynam-ical systems.