Qualitative analysis of a predator–prey system with mutual interference and impulsive state feedback control

Liang, Zhiqing; Pang, Guoping; Zeng, Xiaping; Liang, Yuanbo

doi:10.1007/s11071-016-3129-y

Cited by 11 publications

(5 citation statements)

References 52 publications

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“…Mathematically, impulsive state feedback control of dynamic systems can accurately describe these behaviors. In recent years, great progress has been made in the study of impulsive state feedback control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In [2], the basic theory of impulsive semicontinuous dynamical systems and the existence and stability of periodic solutions of impulsive semicontinuous dynamical systems are introduced.…”

Section: Differential Mean Value Theoremmentioning

confidence: 99%

“…In [2], the basic theory of impulsive semicontinuous dynamical systems and the existence and stability of periodic solutions of impulsive semicontinuous dynamical systems are introduced. In [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], impulsive state feedback controlled dynamic systems were applied in different fields such as vegetation protection, algal fish systems, rare animal protection, and cyber security. Through state feedback pulse control, the interaction between various groups in the aquatic ecosystem can also be adjusted, which helps to maintain the balance and stability of the system.…”

Section: Differential Mean Value Theoremmentioning

confidence: 99%

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Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

Wang¹,

Zhang²

2022

JAMC

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The phenomenon of destroying aquatic ecosystems caused by eutrophication of water occurs from time to time. This paper proposes a prey-predator system with impulsive release of predator populations in polluted water. By constructing Lyapunov function, a sufficient condition for the global asymptotic stability of the system without impulsive effect is obtained. Then, by using the geometric theory of semi-continuous dynamical systems and the successor function method, the existence and uniqueness of the order-1 periodic solution are analyzed, and the stability of the order-1 periodic solution is discussed by using the Analogue of the Poincaré criterion of impulsive differential equations. Finally, we illustrate our theoretical results and biological significance by numerical simulation.

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Section: Differential Mean Value Theoremmentioning

confidence: 99%

Section: Differential Mean Value Theoremmentioning

confidence: 99%

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

Wang¹,

Zhang²

2022

JAMC

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“…Thus we have y C + 2 > y B + 1 , and point C + 2 is close enough to point B + 1 , then we have y C + 2 < y C , that is, g(C) = y C + 2y C < 0. According to [54,Lemma 3.2,3.3], there has a point P ∈ (B + 1 , C) such that g(P) = 0, i.e. system (3) admits the order one periodic orbit, whose initial point is between point B + 1 and point C in the set N (see Fig.…”

Section: Existence Of the Order One Periodic Orbit And Homoclinic Cycmentioning

confidence: 99%

Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent

Shi

Wang

et al. 2019

Adv Differ Equ

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In this paper, a predator-prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the homoclinic cycle is obtained by analyzing the control parameter q. The existence, uniqueness and asymptotic stability of the periodic orbit are discussed by using the geometric theory of the differential equations, the method of successor functions and analog of the Poincaré criterion. Secondly, we formulate a control optimization with a minimal total cost in pest management, and we obtain an optimal economic threshold. Finally, we verify the main results by numerical simulation.

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“…Jiang et al obtained the order-1 periodic solutions using the Poincaré map [18,19], and Chen developed the idea of successor functions to study the mathematical models with pulse state feedback control [20]. Due to its importance in applications, in recent years, systems of impulsive differential equations have attracted more and more attention and been applied to different areas from population dynamics to chemical regulator systems [21][22][23][24][25][26][27][28]. Due to the challenges in analysing these models, most of existing models only considered the population size without considering the population growth rate when proposing a control strategy [29,30].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

Hou

Zhang

et al. 2021

Preprint

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This paper proposes a comprehensive fishing strategy that takes into consideration the population density of fish and its current growth rate, which provides new ideas for fishing strategies. Firstly, we establish a phytoplankton-fish model with the impulsive feedback control depending on the density and rate of change of the fish. Secondly, the complex phase and impulse sets of this model are divided into three cases, then the Poincar´e map for the model is defined, and analyzed the properties of Poincar´e map. In addition, the sufficient and necessary conditions for the global asymptotic stability of the order-1 periodic solution and existence condition of order- k ( k ≥ 2) periodic solution are discussed. The action threshold depends on the density and rate of change of the fish, which is reasonable than earlier studies. The analysis method proposed in this paper also plays an important role in the analysis of impulse models with complex phase sets or impulse sets.

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Qualitative analysis of a predator–prey system with mutual interference and impulsive state feedback control

Cited by 11 publications

References 52 publications

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

Study on Predator-Prey System with Impulsive Release of Predator Population in Polluted Water

Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent

Dynamic Analysis of a Phytoplankton-Fish Model with the Impulsive Feedback Control Depending on the Fish Density and Its Changing Rate

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