A delayed stage-structured predator–prey model with impulsive stocking on prey and continuous harvesting on predator

Jiao, Jianjun; Pang, Guoping; Chen, Lansun; Luo, Guilie

doi:10.1016/j.amc.2007.04.098

Cited by 43 publications

(15 citation statements)

References 15 publications

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“…This model assumes an average age to maturity which appears as a constant time delay reflecting a delayed birth of immature and a reduced survival of immature to their maturity. There are a few papers devote to impulsive delay equations (for example, [2][3][4][5][6][7][8][9]), while with Holling-III functional response and ratio-dependent delayed impulsive equations have not been studied until now. Based on the above discussion, we investigate a delayed ratio-dependent predatorprey system with stage-structured and impulsive effect.…”

Section: Introductionmentioning

confidence: 98%

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

2011

J Syst Sci Complex

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In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable.

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Section: Introductionmentioning

confidence: 98%

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

2011

J Syst Sci Complex

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“…Stage-structured population models have received great attention in recent years [1,6,11,12,18]. Chen et al [6] proposed a stage-structured single-species population model without time delay.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a pest management predator–prey model with stage structure and impulsive stocking

Cai

Jiao

2015

J. Appl. Math. Comput.

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In this work, a pest management predator-prey model with stage structure on prey and impulsive stocking juvenile predator is investigated. By the stroboscopic map of the discrete dynamical system, the prey-extinction periodic solution of the investigated system is proved to be globally attractive. By the theory of impulsive and delay differential equation, the investigated system is also proved to be permanent. Finally, numerical analysis is inserted to illustrate the results. Our conclusions provide reliable tactical basis for the practical pest management.

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“…development, has been studied extensively by many authors [7,13]. But in the natural world, there are many species whose individual members have a life history that takes them through two stages, immature and mature.…”

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confidence: 99%

“…The prey-predator system is a very important model that has been studied by many mathematicians [2,5,7,8,10,12]. Most authors assumed that in the classical model each individual predator admits the same ability to attack the preys.…”

mentioning

confidence: 99%

Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators

Jiao

Cai

Chen

2010

J. Appl. Math. Comput.

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In this work, a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators is investigated. By the stroboscopic map of the discrete dynamical system, the prey-extinction periodic solution of the investigated system is proved to be globally asymptotically stable. By the theory of impulsive differential equation, the investigated system is also proved to be permanent. Finally, the numerical analysis is inserted to illustrate the results. Our conclusions provide reliable tactical basis for the practical biological management.

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A delayed stage-structured predator–prey model with impulsive stocking on prey and continuous harvesting on predator

Cited by 43 publications

References 15 publications

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

Dynamics of a pest management predator–prey model with stage structure and impulsive stocking

Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators

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