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A Nonlinear Predator-Prey System in Deterministic and Stochastic Environment

Alakes Maiti, A. K. Pal, G. P. Samanta

Abstract


The paper aims to study the stability behaviour of a predator-prey system in deterministic and stochastic environment. In deterministic environment, we have studied the boundedness of the system, and stability of its equilibrium points. The growth rate of the prey and the death rate of the predator species are perturbed by Gaussian white noises to simulate a random environment. The resulting model is then cultured by the technique of statistical linearization, and criteria for non-equilibrium fluctuation and stability are derived. Computer simulation is carried out to validate our results on the deterministic stability of the interior equilibrium point. The implications of our analytical findings are discussed critically.

Keywords


stability, white noise, moment equation.

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