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A stochastic model for predator-prey systems: basic properties, stability and computer simulation

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Abstract

A simple stochastic description of a model of a predator-prey system is given. The evolution of the system is described by means of Itô's stochastic differential equations (SDEs), which are the natural stochastic generalization of the Lotka-Volterra deterministic differential equations. Since these SDEs do not satisfy the usual conditions for the existence and uniqueness of the solution, we state a theorem of existence; moreover we study the stability of the equilibrium point and perform a computer simulation to study the behaviour of the trajectories of solutions with given initial data and to estimate first and second moments.

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  1. Dipartimento di Matematica, II University di Roma “Tor Vergata”, Via Fontanile di Carcaricola, I-00133, Roma, Italy

    M. Abundo

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  1. M. Abundo
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Abundo, M. A stochastic model for predator-prey systems: basic properties, stability and computer simulation. J. Math. Biol. 29, 495–511 (1991). https://doi.org/10.1007/BF00164048

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  • DOI: https://doi.org/10.1007/BF00164048

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