Qualitative analysis of a predator–prey model with constant-rate prey harvesting incorporating a constant prey refuge

Ji, Lili; Wu, Chengjiu

doi:10.1016/j.nonrwa.2009.07.003

Cited by 102 publications

(50 citation statements)

References 18 publications

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“…In [15], McNair obtained that a prey refuge with legitimate entry-exit dynamics was capable of amplifying predator-prey oscillations and several kinds of refuges could exert a locally destabilizing effect in [16]. For more biological backgrounds and results on the effects of a prey refuge, one could refer to [5,6,9,[11][12][13] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis on prey refuge in a predator-prey model with square root functional response

Chen¹,

Wang²

2018

J. Math. Computer Sci.

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In this paper, we consider a predator-prey model with square root functional response and prey refuge. The study reveals that the dynamical behavior near the origin of the model is subtle and interesting. We also show that the model undergoes Transcritical bifurcation and Hopf bifurcation. Numerical simulations not only illustrate our results, but also exhibit richer dynamical behaviors of the model than those with Holling II type functional response. Taking prey refuge as control variable, it is feasible to decrease predation rate and then control predator density properly so as to avoid two of population extinction and promote coexistence.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis on prey refuge in a predator-prey model with square root functional response

Chen¹,

Wang²

2018

J. Math. Computer Sci.

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“…The population models with static interactions, like competition, predator-prey, mutualism, is widely and well studied in [2], [6], [7], [11], [14]. However, there are some evidences [5], [12], [13], [14] show that it not adequate the case as the interspecific relationship may change depending on population densities and environmental parameters and so on.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a two-species model with transitions in population interactions

Wang

Xiao

2017

MATEC Web Conf.

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Abstract.A two-species model with variable population interactions and harvesting on one of the species is studied. Existence and stability of equilibria and existence of periodic solutions are established, existence of some bifurcation phenomena are analytically and numerically studied, explicit threshold values are computed to determine the kind of interaction ( mutualism, competition, host-parasite) between the two species. A brief discussion on the influence of the harvesting function on the dynamics of the model is also included.

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“…Since Gause et al [3] and Maynard Smith [4] introduced a quantity x R of the prey that involves refuges, the concept of prey refuges has attracted the attention of ecologists and mathematicians because it exists extensively in predator-prey communities. A lot of literatures showed that prey refuges have significant effects on the population dynamic (see [5,6,7,8,9,10,11,12] in detail). Incorporating prey refuges in the above system, system (1.1) turns into…”

Section: Introductionmentioning

confidence: 99%

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

et al. 2015

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This article concerns with the optimal harvesting of a predator-prey model with prey refuge and imprecise biological parameters. We consider the above model under impreciseness and introduce parametric functional form of an interval which are different from that of models with precise biological parameters. We study the existence and stability of the equilibria. The bionomic equilibria of the model are discussed. Also, the optimal harvesting policy is derived by using Pontryagin's maximal principle. Numerical simulations are presented to verify the feasibility of our analytical results.

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Qualitative analysis of a predator–prey model with constant-rate prey harvesting incorporating a constant prey refuge

Cited by 102 publications

References 18 publications

Dynamical analysis on prey refuge in a predator-prey model with square root functional response

Dynamical analysis on prey refuge in a predator-prey model with square root functional response

Dynamics of a two-species model with transitions in population interactions

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

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