Dynamic analysis of a prey–predator model with state-dependent control strategy and square root response function

Abstract

In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed. Then the stability of the order-1 periodic solution is discussed by the Poincaré criterion for impulsive differential equations. Finally, we show a specific example and carry out numerical simulations to verify the theoretical results.

Dynamic Analysis of Beddington–DeAngelis Predator‐Prey System with Nonlinear Impulse Feedback Control

“…For completeness, we summarize global results for system (3) in Lemma 1 [25,48,49]. In the following parts, we only discuss the case of (u * , v * ) as the globally asymptotically stable point of system (5).…”

“…e predator-prey system plays an important role in the relationship of biological populations, so many predatorprey systems with di erent functional responses have been studied, such as the Monod type [1][2][3][4][5], the Holling type [6][7][8][9][10][11][12][13], and the Ivlev type [14][15][16][17][18]. Currently, the use of chemicals is more and more widespread in agriculture.…”

Dynamics in a diffusive phytoplankton–zooplankton system with time delay and harvesting

“…The functional response of predators to prey density is important for predator-prey models [22][23][24][25]. In ecology, many factors, such as predator hunting ability, prey escape ability, and structure of the prey habitat, can affect functional responses.…”

Stability Analysis and Control Optimization of a Prey-Predator Model with Linear Feedback Control

“…In the practical production, effective control of pests is a very important issue of the world, which catches attention of scholars for pest management method [1][2][3][4][5][6][7]. Integrated pest management (IPM), also known as integrated pest control (IPC), is an effective approach that integrates biological, chemical tactics, and physical methods for pests control [8][9][10][11]. Due to population dynamics and its related environment, IPM utilize effective methods and techniques comprehensively to reduce the level of economic harm caused by pests.…”