Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse

Abstract

In this paper, a predator-prey model with Holling type-I functional response and multi state impulsive feedback control is established, where the intensity of pesticide spraying and the release amount of natural enemies are linearly dependent on the given threshold in the second impulse. Firstly, the existence of order-1 periodic solution of the system is investigated by successor functions and Bendixson theorem of impulsive differential equations, then the stability of periodic solutions is proved by the analogue of the Poincaré criterion. Furthermore, in order to reduce the actual total cost and obtain the best economic benefit, the optimal economic threshold is obtained, which provides the optimal strategy for the practical application. Finally, numerical simulations for specific examples are carried out to illustrate the feasibility of the above conclusions.

The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control

“…Once the weighted parameter vanishes, i.e., 훽 = 0 the action threshold just relies upon the density of pest population. en the action threshold will be transformed into ET, which has been extensively demonstrated and explored in past writings [39][40][41][42][43][44][45]. e reason for choosing ratio-dependent AT is the presence of some practical issues in the previous used models during investigation on this topic.…”

“…In all the previous literatures, researchers projected models either with a single economic threshold or multiple thresholds [39][40][41][42][43][44][45]. ere are few drawbacks to this sort of thresholds.…”

Dynamical analysis of a logistic model with impulsive Holling type-II harvesting

“…It is often the case that harvesting occurs at fixed moments every year, which brings about short-term rapid changes for the densities of the species. Impulsive differential systems are suitable for the mathematical simulation of this evolutionary process ( [3][4][5][6][7][8][9][10][11][12][13][14][28][29][30][31][32][33][34][35][36][37][38][39]). In this paper, we propose the following autonomous logistic model with regular harvest pulse: 4) together with the initial condition…”

A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

“…By using (8)- (10) Besov spaces , (R 2 ) for 0 < < 1 and 1 < , < ∞. For other interesting works on this topic we refer the readers to consult [24][25][26][27][28]. We denote by , (R ) the fractional Sobolev spaces defined by the Bessel potentials.…”