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A modified Holling-Tanner model in stochastic environment. (English) Zbl 1188.93015

Summary: Recently, a modified version of the so called Holling-Tanner model is introduced in the ecological literature. A detailed account of the deterministic dynamics of this model is presented. The growth rates of the prey and predator are then perturbed by Gaussian white noises to take into account the effect of fluctuating environment. The resulting stochastic model is transformed by the technique of statistical linearization and criteria for non-equilibrium fluctuation and stability are derived. Numerical simulations are carried out. The implications of our analytical findings are addressed critically.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
93E03 Stochastic systems in control theory (general)
93E12 Identification in stochastic control theory
92D40 Ecology
49N75 Pursuit and evasion games
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