Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

Zhang, Shengqiang; Meng, Xinzhu; Feng, Tao; Zhang, Tonghua

doi:10.1016/j.nahs.2017.04.003

Cited by 159 publications

(63 citation statements)

References 28 publications

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“…And due to the seasonal and economic reasons, periodic harvesting is an effective harvesting strategy for the infrequent harvesting. This periodic harvesting can be described by impulsive differential equations [9][10][11][12][13][14][15][16]. There are some papers studying the effects of periodic impulse harvesting strategy to the species resource.…”

Section: Introductionmentioning

confidence: 99%

Periodic solution and control optimization of a prey-predator model with two types of harvesting

et al. 2018

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In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.

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Section: Introductionmentioning

confidence: 99%

Periodic solution and control optimization of a prey-predator model with two types of harvesting

et al. 2018

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“…With this in mind, the mathematical model of diffusion with pulse has been established, which makes the research more significant [6][7][8][9][10][11][12][13][14]. In particular, impulsive differential equations are very important in the research of population migration phenomenon [15][16][17][18][19][20][21][22][23][24]. Jiao et al [25] established a SIR model with pulse vaccination and proved the existence of a disease-free periodic solution, and a large pulse vaccination rate was a sufficient condition to eradicate the disease.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

Cheng

Wang

et al. 2018

Adv Differ Equ

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In this paper, we establish a unilateral diffusion Gompertz model of a single population in two patches in a theoretical way. Firstly, we prove the existence and uniqueness of an order-one periodic solution by the geometry theory of differential equations and the method of successor function. Secondly, we prove the stability of the order-one periodic solution by imitating the theory of the limit cycle of an ordinary differential equation. Finally, we verify the theoretical results by numerical simulations.

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“…Hence, many authors have introduced stochastic interferences into differential systems, and the stochastic dynamics of such systems were widely investigated (see [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). Moreover, numerous scholars have investigated some stochastic epidemic models (see [29][30][31][32][33][34]).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, many scholars focused on nonautonomous stochastic periodic systems. With the development of stochastic differential equations and application of Has'minskii theory, the existence of stochastic periodic solution has been studied [23,38,39]. In [23], Zhang et al considered a nonautonomous stochastic Lotka-Volterra predator-prey model with impulsive effects; they got thresholds for stochastic persistence and extinction of the system.…”

Section: Introductionmentioning

confidence: 99%

“…With the development of stochastic differential equations and application of Has'minskii theory, the existence of stochastic periodic solution has been studied [23,38,39]. In [23], Zhang et al considered a nonautonomous stochastic Lotka-Volterra predator-prey model with impulsive effects; they got thresholds for stochastic persistence and extinction of the system. Authors of [38][39][40] investigated periodic solution of a stochastic nonautonomous epidemic model.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Liu

Meng

2017

Complexity

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We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has'minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

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Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

Cited by 159 publications

References 28 publications

Periodic solution and control optimization of a prey-predator model with two types of harvesting

Periodic solution and control optimization of a prey-predator model with two types of harvesting

Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

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