Extinction in a generalized Lotka-Volterra predator-prey model.
Ackleh, Azmy S., Marshall, David F., Heatherly, Henry E. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Ackleh, Azmy S., Marshall, David F., Heatherly, Henry E. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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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...
Joanna Pętela (2010)
Applicationes Mathematicae
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We consider nonautonomous competitive Kolmogorov systems, which are generalizations of the classical Lotka-Volterra competition model. Applying Ahmad and Lazer's definitions of lower and upper averages of a function, we give an average condition which guarantees that all but one of the species are driven to extinction.
Nolting, Ben, Paullet, Joseph E., Previte, Joseph P. (2008)
Applied Mathematics E-Notes [electronic only]
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Janusz Szwabiński, Andrzej Pękalski, Kamil Trojan (2008)
Banach Center Publications
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A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.
J. P. Gill, K. M. Shaw, B. L. Rountree, C. E. Kehl, H. J. Chiel (2011)
Mathematical Modelling of Natural Phenomena
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We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown ...
Samanta, G.P. (2010)
International Journal of Mathematics and Mathematical Sciences
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Y. Tyutyunov, L. Titova, R. Arditi (2010)
Mathematical Modelling of Natural Phenomena
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A conceptual minimal model demonstrating spatially heterogeneous wave regimes interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The model is based on the earlier proposed hypothesis that taxis accelerations of prey and predators are proportional to the density gradient of another population playing a role of taxis stimulus. Considering acceleration rather than immediate velocity allows obtaining realistic solutions even while ignoring variations...
Julián López-Gómez, Rosa Pardo (1991)
Extracta Mathematicae
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We solve the problem of the existence and uniqueness of coexistence states for the classical predator-prey model of Lotka-Volterra with diffusion in the scalar case.