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Comparing stochastic Lotka–Volterra predator-prey models

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  • Vadillo, Fernando

Abstract

The phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event. In the present investigation, we study this problem for three different stochastic models built from a single Lotka–Volterra deterministic model. More concretely, we study their mean-extinction time which satisfies the backward Kolmogorov differential equation, a linear second-order partial differential equation with variable coefficients; hence, we can only compute numerical approximations. We suggest a finite element method using FreeFem++. Our analysis and numerical results allow us to conclude that there are important differences between the three models. These differences enable us to choose the most “natural way” to turn a the deterministic model into a stochastic model.

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  • Vadillo, Fernando, 2019. "Comparing stochastic Lotka–Volterra predator-prey models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 181-189.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:181-189
    DOI: 10.1016/j.amc.2019.05.002
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    1. Skvortsov, Alex & Ristic, Branko & Kamenev, Alex, 2018. "Predicting population extinction from early observations of the Lotka–Volterra system," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 371-379.
    2. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    3. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    1. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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