Dynamical properties of a delay prey-predator model with disease in the prey species only.
Shi, Xiangyun, Zhou, Xueyong, Song, Xinyu (2010)
Discrete Dynamics in Nature and Society
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Shi, Xiangyun, Zhou, Xueyong, Song, Xinyu (2010)
Discrete Dynamics in Nature and Society
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Huo, Hai-Feng, Ma, Zhan-Ping, Liu, Chun-Ying (2009)
Abstract and Applied Analysis
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Joydeb Bhattacharyya, Samares Pal (2013)
Applicationes Mathematicae
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A three dimensional predator-prey-resource model is proposed and analyzed to study the dynamics of the system with resource-dependent yields of the organisms. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more of the predators and in the presence of all the predators....
Bhattacharyya, Rakhi, Mukhopadhyay, Banibrata, Bandyopadhyay, Malay (2003)
International Journal of Mathematics and Mathematical Sciences
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Debasis Mukherjee (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.
Cai, Liming, Li, Xuezhi, Song, Xinyu, Yu, Jingyuan (2007)
Discrete Dynamics in Nature and Society
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Wu, Huiling, Chen, Fengde (2009)
Discrete Dynamics in Nature and Society
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Xue, Yakui, Duan, Xiafeng (2011)
Discrete Dynamics in Nature and Society
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El-Owaidy, Hassan M., Moniem, Ashraf A. (2003)
Applied Mathematics E-Notes [electronic only]
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D. Bontje, B. W. Kooi, G. A.K. van Voorn, S.A.L.M Kooijman (2009)
Mathematical Modelling of Natural Phenomena
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Since Rosenzweig showed the destabilisation of exploited ecosystems, the so called , several mechanisms have been proposed to resolve this paradox. In this paper we will show that a feeding threshold in the functional response for predators feeding on a prey population stabilizes the system and that there exists a minimum threshold value above which the predator-prey system is unconditionally stable with respect to enrichment. Two models are analysed, the first being the classical Rosenzweig-MacArthur...
Song, Xinyu, Ge, Zhihao, Wu, Jingang (2006)
International Journal of Mathematics and Mathematical Sciences
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Tapan Kumar Kar (2005)
Applicationes Mathematicae
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The dynamics of a prey-predator system, where predator has two stages, a juvenile stage and a mature stage, is modelled by a system of three ordinary differential equations. Stability and permanence of the system are discussed. Furthermore, we consider the harvesting of prey species and obtain the maximum sustainable yield and the optimal harvesting policy.