Using non-smooth models to determine thresholds for microbial pest management

Wang, Aili; Xiao, Yanni; Smith, Robert J.

doi:10.1007/s00285-018-1313-z

Cited by 13 publications

(2 citation statements)

References 39 publications

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“…Usually, this instantaneous change is a result of some external effect on the system, which has a duration that is negligible compared to the overall time scale of the process. Impulsive DEs have many practical applications such as pest control [4], pulse vaccination strategies [5], and optimal harvesting in fisheries [6]. For more on the theory of impulsive DEs see the monograph [7].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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“…The impulsive differential equations have even been intensively studied in recent two decades, especially for state-dependent impulsive equations, which means the impulsive control takes place when a certain state is met [4,5,8,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]26]. However, because of the discontinuity of the system, the issue becomes more complicated but not less important than a continuous one.…”

Section: Introductionmentioning

confidence: 99%

The state-dependent impulsive control for a general predator–prey model

Zhu

Wang

Ouyang

2021

Journal of Biological Dynamics

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In this paper, a general predator-prey model with state-dependent impulse is considered. Based on the geometric analysis and Poincaré map or successor function, we construct three typical types of Bendixson domains to obtain some sufficient conditions for the existence of order-1 periodic solutions. At the same time, the existing domains are discussed with respect to the system parameters. Moreover, the Analogue of Poincaré Criterion is used to obtain the asymptotic stability of the periodic solutions. Finally, to illustrate the results, an example is presented and some numerical simulations are carried out.

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