Biocontrol in an impulsive predator-prey model

Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results.

Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate

This work presents a pest control predator-prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results.