The dynamical behavior of a predator–prey system with Gompertz growth function and impulsive dispersal of prey between two patches

An almost periodic predator-prey model with intermittent predation and prey discontinuous dispersal is studied in this paper, which differs from the classical continuous and impulsive dispersal predator-prey models. The intermittent predation behavior of the predator species only happens in the channels between two patches where the discontinuous migration movement of the prey species occurs. Using analytic approaches and comparison theorems of the impulsive differential equations, sufficient criteria on the boundedness, permanence, and coexistence for this system are established. Finally, numerical simulations demonstrate that, for an intermittent predator-prey model, both the intermittent predation and intrinsic growth rates of the prey and predator species can greatly impact the permanence, extinction, and coexistence of the population.

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“…Suppose ( 1 ( ), 2 ( ), ( )) is arbitrary positive solution of system (4); from above inequalities (24), (31), and (35), we have…”

Section: Theorem 11 Suppose That Assumptions ( 1 )-( 7 ) and The Folmentioning

confidence: 99%

“…Currently, theories of impulsive differential equations [16] have been introduced into population dynamics. A large number of models have been described by impulsive diffusion (see [14,[17][18][19][20][21][22][23][24]) during the past couple of decades.…”

Section: Introductionmentioning

confidence: 99%

Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal

Luo

Zhang

Teng

et al. 2017

Discrete Dynamics in Nature and Society

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“…Compared with the logistic function, it has been proven to be a simple example to generate an asymmetric S-shaped curve [22]. Since then, many models have been established for biological growth by using the Gompertz function (e.g., [23,24]). Furthermore, many species usually go through two distinct life stages, immature and mature.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches

Zhang

et al. 2020

Discrete Dynamics in Nature and Society

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In this paper, we consider a hybrid network model of delayed predator-prey Gompertz systems with impulsive diffusion between two patches, in which the patches represent nodes of the network such that the prey population interacts locally in each patch and diffusion occurs along the edges connecting the nodes. Using the discrete dynamical system determined by the stroboscopic map which has a globally stable positive fixed point, we obtain the global attractive condition of predator-extinction periodic solution for the network system. Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.

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“…It is well known that mathematical model is a powerful tool to investigate the interior of the endemic transmission dynamics . The first model of schistosomiasis was proposed by Macdonald in 1965 .…”

Section: Introductionmentioning

confidence: 99%

A schistosomiasis compartment model with incubation and its optimal control

Ding

Sun

Zhu

2017

Math Methods in App Sciences

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A new mathematical model included an exposed compartment is established in consideration of incubation period of schistosoma in human body. The basic reproduction number is calculated to illustrate the threshold of disease outbreak. The existence of the disease free equilibrium and the endemic equilibrium are proved. Studies about stability behaviors of the model are exploited. Moreover, control measure assessments are investigated in order to seek out effective control interventions for anti‐schistosomiasis. Then, the corresponding optimal control problem according to the model is presented and solved. Theoretical analyses and numerical simulations induce several prevention and control strategies for anti‐schistosomiasis. At last, a discussion is provided about our results and further work. Copyright © 2017 John Wiley & Sons, Ltd.

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The dynamical behavior of a predator–prey system with Gompertz growth function and impulsive dispersal of prey between two patches

Cited by 14 publications

References 39 publications

Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal

Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal

Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches

A schistosomiasis compartment model with incubation and its optimal control

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