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MEAN SQUARE STABILITY IN A MODIFIED LESLIE-GOWER AND HOLLING-TYPE II PREDATOR-PREY MODEL
Pallav Jyoti Pal,Sahabuddin Sarwardi,Tapan Saha,Prashanta Kumar Mandal 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3
Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.
MEAN SQUARE STABILITY IN A MODIFIED LESLIE-GOWER AND HOLLING-TYPE II PREDATOR-PREY MODEL
Pal, Pallav Jyoti,Sarwardi, Sahabuddin,Saha, Tapan,Mandal, Prashanta Kumar The Korean Society of Computational and Applied Ma 2011 Journal of applied mathematics & informatics Vol.29 No.3
Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.