Modelling and analysis of a prey–predator system with stage-structure and harvesting

Kar, Tapan Kumar; Pahari, U. K.

doi:10.1016/j.nonrwa.2006.01.004

Cited by 86 publications

(62 citation statements)

References 18 publications

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“…58, No.4B, pp: 2177-2187 2178 considered stage or structure to formulate the problem in their models for more details see [3][4][5][6][7][8][9][10]. In [11], the author has been studied the same model with optimal control in continuous time form.…”

Section: Issn: 0067-2904mentioning

confidence: 99%

The Dynamics of Discrete System with Constant Rate Harvesting

2017

ijs

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In this papera prey -predator discrete dynamical system with Holling type I functional response is presented . The existence of all possibleequilibria have been obtained algebraically. The model has four equilibriaand some conditions for the local stability of its equilibria have been established. We see that the proposed model has rich dynamics behavior. Aconstant rate harvesting for a single population is also considered as well as the exitence of the bionomic equilibrium is dicussed and computed. The numerical simulation is given to conforim the theoretical analysis stability of the model.Finally a general disscution is provided.

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Section: Issn: 0067-2904mentioning

confidence: 99%

The Dynamics of Discrete System with Constant Rate Harvesting

2017

ijs

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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%

“…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. The literatures [7][8][9][10] proposed and investigated the dynamics of predator-prey models with harvesting and stage structure. Although these established models with stage structure is different, but all assume that only mature predator is capable of preying on prey, which is inconsistent with observed fact.…”

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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“…Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Also Kar [14], Kar and Matsuda [15], Kar and Pahari [16,17], Kar and Ghorai [18], Kuang [19], and some other authors have discussed delayed predator-prey system.…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

Das

Kar

2014

Journal of Nonlinear Dynamics

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This paper tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results.

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Modelling and analysis of a prey–predator system with stage-structure and harvesting

Cited by 86 publications

References 18 publications

The Dynamics of Discrete System with Constant Rate Harvesting

The Dynamics of Discrete System with Constant Rate Harvesting

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

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

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