Abstract
Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models.
Highlights
Pest control [1,2,3,4,5,6] is an ancient problem and a new challenge faced by the modern world
Maiti et al [19] used a valuable technique known as sterile insect release method (SIRM) to manage the pest population. e authors discussed the effect of uncertain ecological variations on sterile and fertile insects
If the control strategy is not implemented in time, it may lead to a large outbreak of pests
Summary
Pest control [1,2,3,4,5,6] is an ancient problem and a new challenge faced by the modern world. Is is one of the most useful methods which minimizes damage to individuals and the environment in addressing pest control In this perspective, researchers have studied the mathematical problems based on impulsive differential equations in order investigate the dynamics of IPM and compass biped robotic systems. A fundamental problem illustrated by these two situations is that when the pest population is large (such as exceeding ET), the growth rate is small or even negative at this time In this case, even if the IPM strategy is not implemented, the number of pests may not exceed economic injury level (EIL) [36]. By using the analytical properties of Poincaremap, the existence, uniqueness, and stability of the pest-free and interior-order one periodic solution of the pest-natural enemy system are given, and corresponding sufficient conditions are obtained. e main results are confirmed by numerical simulations
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