Global Stability of a Predator-Prey System with Stage Structure for the Predator

Xiao, Yan; Chen, Lansun

doi:10.1007/s10114-002-0234-2

Cited by 55 publications

(45 citation statements)

References 9 publications

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“…If the system is locally asymptotically stable at E * and the conditions for permanence and competitiveness are satisfied, then E * is globally asymptotically stable [26]. …”

Section: Lemma 47mentioning

confidence: 99%

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

Bhattacharyya

Pal

2012

J Biol Phys

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A three-dimensional stage-structured predator-prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.

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“…If the system is locally asymptotically stable at E * and the conditions for permanence and competitiveness are satisfied, then E * is globally asymptotically stable [26]. …”

Section: Lemma 47mentioning

confidence: 99%

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

Bhattacharyya

Pal

2012

J Biol Phys

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“…Since W. G. Aiello and H. I. Freedman [1] built and studied a time delay model of single species growth with stage structure, model with stage structure consisting of immature and mature stages has been paid many attentions by numerous scholars due to it embodies the specific stages in different habits of its whole life history of biological population (particularly mammalian population) in the natural world: see [2][3][4][5][6][7][8][9][10] and references therein. The authors in [2][3][4] studied the global properties and the existence and stability of periodic solutions of a predatorprey model with nonlinear functional response and stage structure for the predator.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in [2][3][4] studied the global properties and the existence and stability of periodic solutions of a predatorprey model with nonlinear functional response and stage structure for the predator. W. Wang, et al [5] and R. Xu, et al [6] showed the combined effects of stage structure for predator and time delay on the global dynamics of predator-prey model.…”

Section: Introductionmentioning

confidence: 99%

Global dynmics of of a syrphid fly-aphid model with stage structure for predator popoluation

2017

J. Nonlinear Funct. Anal.

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Abstract. A syrphid fly-aphid model with stage structure for predator population is considered, in which only the immature predator-natural enemy syrphid fly can prey on pest-aphid. By applying Lyapunov functions and LaSalles invariance principle, we show that the global asymptotic stability of the interior equilibrium for the considered model. We also obtain results on the existence and stability of periodic solutions. Numerical simulations are also performed to illustrate the validity of our results.

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“…Persistence (or permanence) is an important property of dynamical systems, in this section, we focus on the permanence of system (3). Denote S t I t of (3) satisfies ( ) S t q  , for sufficiently large t .…”

Section: Permanencementioning

confidence: 99%

“…Pest control strategies have been attracted many experts over the past years. Recently, stage-structured models have received much attraction [2,3]. However, the epidemic models with stage-structure have been seldom studied.…”

Section: Introductionmentioning

confidence: 99%

A Pest Management Epidemic Model with Time Delay and Stage-Structure

Gao¹,

Liu²,

Lan³

2010

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In this paper, an SI epidemic model with stage structure is investigated. In this model, impulsive biological control which release infected pest to the field at a fixed time periodically is considered, and obtained the sufficient conditions for the global attractivity of pest-extinction periodic solution and permanence of the system. We also prove that all solutions of the model are uniformly ultimately bounded. The sensitive analysis on the two thresholds and to the changes of the releasing amounts of infected pest is shown by numerical simulations. Our results provide a reliable tactic basis for the practice of pest management.

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Global Stability of a Predator-Prey System with Stage Structure for the Predator

Cited by 55 publications

References 9 publications

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

Global dynmics of of a syrphid fly-aphid model with stage structure for predator popoluation

A Pest Management Epidemic Model with Time Delay and Stage-Structure

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