Comparing stochastic Lotka–Volterra predator-prey models

Fernando Vadillo

Applied Mathematics and Computation, 2019, vol. 360, issue C, 181-189

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.

Keywords: Extinction-time; Population models; Stochastic Differential Equations; Finite Elements Method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:360:y:2019:i:c:p:181-189

DOI: 10.1016/j.amc.2019.05.002

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