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Deterministic chaos versus stochastic oscillation in a prey-predator-top predator model

    Ranjit Kumar Upadhyay Affiliation
    ; Malay Banerjee Affiliation
    ; Rana Parshad Affiliation
    ; Sharada Nandan Raw Affiliation

Abstract

The main objective of the present paper is to consider the dynamical analysis of a three dimensional prey-predator model within deterministic environment and the influence of environmental driving forces on the dynamics of the model system. For the deterministic model we have obtained the local asymptotic stability criteria of various equilibrium points and derived the condition for the existence of small amplitude periodic solution bifurcating from interior equilibrium point through Hopf bifurcation. We have obtained the parametric domain within which the model system exhibit chaotic oscillation and determined the route to chaos. Finally, we have shown that chaotic oscillation disappears in presence of environmental driving forces which actually affect the deterministic growth rates. These driving forces are unable to drive the system from a regime of deterministic chaos towards a stochastically stable situation. The stochastic stability results are discussed in terms of the stability of first and second order moments. Exhaustive numerical simulations are carried out to validate the analytical findings.

Keyword : Deterministic chaos, stochastic oscillation, Hopf bifurcation, Holling type IV functional response

How to Cite
Upadhyay, R., Banerjee, M., Parshad, R., & Raw, S. (2011). Deterministic chaos versus stochastic oscillation in a prey-predator-top predator model. Mathematical Modelling and Analysis, 16(3), 343-364. https://doi.org/10.3846/13926292.2011.601767
Published in Issue
Aug 24, 2011
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