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A detailed study of the Beddington–DeAngelis predator–prey model

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A detailed study of the Beddington–DeAngelis predator–prey model. / Haque, Mainul.

In: Mathematical Biosciences, Vol. 234, No. 1, 01.11.2011, p. 1-16.

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Haque, Mainul. / A detailed study of the Beddington–DeAngelis predator–prey model. In: Mathematical Biosciences. 2011 ; Vol. 234, No. 1. pp. 1-16.

Bibtex

@article{af62fb674231405e9889aa57daa4ba41,
title = "A detailed study of the Beddington–DeAngelis predator–prey model",
abstract = "The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington–DeAngelis predator–prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf–Andronov, Bogdanov–Takens) analysis of this model are conducted. Corresponding results from previous well known predator–prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated “white” noise and correlated “coloured” noise. This showing that competition among the predator population is beneficial for a number of predator–prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator–prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper.",
author = "Mainul Haque",
year = "2011",
month = nov,
day = "1",
doi = "10.1016/j.mbs.2011.07.003",
language = "English",
volume = "234",
pages = "1--16",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - A detailed study of the Beddington–DeAngelis predator–prey model

AU - Haque, Mainul

PY - 2011/11/1

Y1 - 2011/11/1

N2 - The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington–DeAngelis predator–prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf–Andronov, Bogdanov–Takens) analysis of this model are conducted. Corresponding results from previous well known predator–prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated “white” noise and correlated “coloured” noise. This showing that competition among the predator population is beneficial for a number of predator–prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator–prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper.

AB - The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington–DeAngelis predator–prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf–Andronov, Bogdanov–Takens) analysis of this model are conducted. Corresponding results from previous well known predator–prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated “white” noise and correlated “coloured” noise. This showing that competition among the predator population is beneficial for a number of predator–prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator–prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper.

U2 - 10.1016/j.mbs.2011.07.003

DO - 10.1016/j.mbs.2011.07.003

M3 - Article

VL - 234

SP - 1

EP - 16

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -

ID: 13004284