Dynamic behaviors of the periodic predator–prey system with distributed time delays and impulsive effect

Chen, Lijuan; Chen, Fengde

doi:10.1016/j.nonrwa.2011.03.002

Cited by 27 publications

(12 citation statements)

References 22 publications

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“…In natural world, due to individual life cycle and seasonal variation, the carrying capacity of species, birth rate, and other parameters always present periodic changes for population systems [16][17][18]. For the determinate biological system, the existence of periodic solution is a very important dynamical behavior [10,[19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction

Kong

Shao

2020

Discrete Dynamics in Nature and Society

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Considering periodic environmental changes and random disturbance, we explore the dynamical behaviors of a stochastic competitive system with impulsive and periodic parameters in this paper. Firstly, by use of extreme-value theory of quadratic function and constructing suitable functional, we study the existence of periodic Markovian process. Secondly, by comparison theory of the stochastic differential equation, we study the extinction and permanence in the mean of all species. Thirdly, applying an important lemma, we investigate the stochastic persistence of this system. Finally, some numerical simulations are given to illustrate the main results.

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Section: Introductionmentioning

confidence: 99%

Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction

Kong

Shao

2020

Discrete Dynamics in Nature and Society

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“…The predator-prey model is one of the basic models between different species in nature which has been widely researched [1][2][3][4][5][6]. In the natural world, the population generally has a saturation effect.…”

Section: Introductionmentioning

confidence: 99%

“…In most of ecosystems, maturation, pregnancy, and hunting occur all the time. Hence, time delay due to gestation has been greatly researched as a focus issue in a predator-prey system [2][3][4][5][30][31][32], since the current birth rate of the predator is related to its consumption of prey throughout the past history. Chen and Zhang [33] proposed a predator-prey model incorporating delay and predator migration, which can be used to describe biological control.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

2018

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In this paper, we consider a Holling type II predator-prey model incorporating time delay and Allee effect in prey. We discuss the influence of Allee effect on the logistic equation. By analyzing the characteristic equation of the corresponding linearized system, we give the threshold condition for the local asymptotic stability of the system according to the change of birth rate or Allee effect in prey. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. In addition, we show that if the Allee effect is large or the birth rate is small, then both predators and prey are extinct. The Allee effect can influence the stability of the system.

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“…Kuang [22] has pointed out that ignoring time delays means ignoring the reality. Therefore, it is essential to take into account the influence of time delays in the biological modeling [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal harvesting of a stochastic three-species cooperative system with delays and Lévy jumps

2018

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A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species, and the stochastic permanence of this system. Secondly, by applying asymptotic method, we investigate the stability in distribution of solutions. Thirdly, utilizing ergodic method, we obtain the optimal harvesting policy of this system. Finally, some numerical examples are given to illustrate our main results.

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Dynamic behaviors of the periodic predator–prey system with distributed time delays and impulsive effect

Cited by 27 publications

References 22 publications

Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction

Stochastic Periodic Solution and Persistence of a Nonautonomous Impulsive System with Nonlinear Self-Interaction

Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

Dynamical analysis and optimal harvesting of a stochastic three-species cooperative system with delays and Lévy jumps

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