Analysis of a predator-prey model with impulsive diffusion and releasing on predator population

Zhou, Airen; Sattayatham, Pairote; Jiao, Jianjun

doi:10.1186/s13662-016-0834-2

Cited by 2 publications

(6 citation statements)

References 28 publications

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“…Firstly, similar to the literature [18], we can demonstrate that all solutions of (1) are uniformly ultimately bounded. Lemma 1.…”

Section: The Lemmassupporting

confidence: 67%

“…is the capture rate of predators in the ith patch, and k i (i = 1, 2) is the rate of conversion of nutrients into the reproduction rate of predators in the ith patch [18].…”

Section: The Modelmentioning

confidence: 99%

“…for sufficiently large values of t. To simplify the analysis, we can consider that Equation ( 18) holds for all t greater than or equal to zero. By combining Equations ( 1) and (18), we obtain…”

Section: The Dynamicsmentioning

confidence: 99%

“…The measures taken by integrated pest management mainly include tools of chemical control, biological control, cultural control, mechanical or physical control, genetic control, etc. In recent years, the models of integrated pest management have been extensively and deeply studied by many scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions

Zhou

2023

Mathematics

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This paper investigates an integrated pest management model with pulsed diffusion. As we all know, humans have been fighting against pests since they entered the age of farming. When pests are controlled, humans can achieve better harvests. We use the stroboscopic mapping of discrete dynamic system to obtain some important lemmas. Based on the lemmas, firstly, we give the conditions for the global asymptotic stability of the periodic solution of the pest eradication boundary; secondly, the conditions for the permanence of the investigated system are derived; thirdly, numerical simulations are used to verify our obtained theoretical results; finally, increased dispersal was found to have the opposite effect on integrated pest management. We conclude that a combination of impulsive diffusion, spraying pesticides, and releasing natural enemies can play a crucial role in integrated pest management.

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“…Firstly, similar to the literature [18], we can demonstrate that all solutions of (1) are uniformly ultimately bounded. Lemma 1.…”

Section: The Lemmassupporting

confidence: 67%

“…is the capture rate of predators in the ith patch, and k i (i = 1, 2) is the rate of conversion of nutrients into the reproduction rate of predators in the ith patch [18].…”

Section: The Modelmentioning

confidence: 99%

Section: The Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions

Zhou

2023

Mathematics

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“…The functions on the right-hand sides of the former four equations in system (1) are denoted by f = (f 1 , f 2 , f 3 , f 4 ) T . Let V 0 be the set of functions V : R + × R 4 + → R + having the following properties [11,[14][15][16][17]:…”

Section: Preliminariesmentioning

confidence: 99%

An application of the impulsive CSOH model for managing squirrels in the coconut farm

2019

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In this work, we formulate the mathematical model that incorporates two equations to represent the ultimate goal and controlling strategy to the traditional prey-predator model so that we can investigate the interaction between preys and predators. The model is shortly called the CSOH model. The impulsive practice is added into the model for squirrel control purposes. In particular, we are interested in pulsing the squirrel hunters into the system for every fixed period to control squirrels at the level allowing farmers to have sufficient amount of coconuts so that they can continue their business. We establish the conditions for the squirrel-free periodic solution exists and is globally stable. The numerical simulations reveal that squirrels in the coconut farm could be entirely eradicated by the pulsing strategy. However, the disappearance of squirrels on the farm is not an ecological desire because all species should be allowed to coexist in the system. Consequently, we recommend that the number of squirrel hunters pulsed into the coconut farm should be properly set by considering the time of intervention, expenditure, ecological reasons, and emotional sensitivity of village members.

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Analysis of a predator-prey model with impulsive diffusion and releasing on predator population

Cited by 2 publications

References 28 publications

Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions

Analysis of an Integrated Pest Management Model with Impulsive Diffusion between Two Regions

An application of the impulsive CSOH model for managing squirrels in the coconut farm

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