Extinction and permanence of the predator-prey system with general functional response and impulsive control

Liu, Juan; Hu, Jie; Yuen, Peter W. T.

doi:10.1016/j.apm.2020.06.033

Cited by 14 publications

(4 citation statements)

References 30 publications

(56 reference statements)

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“…• predator-prey systems where either one of the species or both are subject to harvesting, structured and Lotka-Volterra models which -without delay in impulsive harvesting or an impulsive system with continuous harvesting -are well-studied areas, see, for example, [9,34,35,36,37,38,39,40,41,42];…”

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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We consider a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of high-order difference equations is used to conclude that while the inclusion of a delay in the impulsive condition does not impact the optimality of the yield, sustainability may be highly affected and is generally delay-dependent. Maximal and other types of yields are explored, and sharp stability tests are obtained for the model, as well as explicit sufficient conditions. It is also shown that persistence of the solution is not guaranteed for all positive initial conditions, and extinction in finite time is possible, as is illustrated in the simulations.

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Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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“…In general, they are exploited to describe the phenomena depending upon steep or instantaneous changes which make the differential system more intractable. A large number of researchers have suggested to apply an impulsive control strategy [50][51][52][53][54] to a modified predator-prey model for obtaining some desired results such as a reduction in pest populations in a farm. This approach is known as integrated pest management (IPM), which is a suitable method for manipulating pests (or preys) with a combination of biological, cultural, physical and chemical tools so that one can minimize economic, health and environmental risks [51,55].…”

Section: Impulsive Model Formulationmentioning

confidence: 99%

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021

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In the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

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“…IPM is aimed at integrating suitable measures, such as chemical and biological methods, to manage the number of pests below EIL(Economic Injury Level) instead of killing off them, thereby not only avoiding economic losses but also contributing to the sustainable development of agroecosystem [11,12]. Actually, taking measures when the number of pests approaches to EIL cannot prevent the economic toll timely, so the Economic Threshold(ET < EIL) is set as a critical value, that is, once the pest population exceeds ET, appropriate measures should be applied to reduce the quantity below ET, which can ensure that EIL is never possible for the pest population to reach [13].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a non-smooth pest-natural enemy model with the threshold control strategy

2023

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Pest issues have always been the focus of attention in agriculture. The integrated Pest Management(IPM) method is currently the most popular way to be applied for pest control. In this study, according to the IPM strategy, we regard pest quantity as a threshold index and extend the Leslie-Gower model into a non-smooth Filippov system through combining chemical and biological control. To maintain the pest population at or below the given economic threshold(ET), we investigate the global dynamics of the proposed model, including the existence of sliding mode and various equilibria, sliding dynamics and bifurcations, and global stability of equilibria. The result shows that desired equilibria can be globally stable under some conditions, meaning that our control tactics work. In particular, the case where our strategy fails to be effective arouses interest. In the end, the biological implications of the results are discussed and given in detail.

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Extinction and permanence of the predator-prey system with general functional response and impulsive control

Cited by 14 publications

References 30 publications

Optimality and sustainability of delayed impulsive harvesting

Optimality and sustainability of delayed impulsive harvesting

Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

Dynamics of a non-smooth pest-natural enemy model with the threshold control strategy

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