Chaotic dynamics of a three species prey–predator competition model with bionomic harvesting due to delayed environmental noise as external driving force - 30/08/12

Doi : 10.1016/j.crvi.2012.06.001

Kalyan Das ^a,^⁎ , M.N. Srinivas ^b , M.A.S. Srinivas ^c , N.H. Gazi ^d
^a National Institute of Food Technology Entrepreneurship and Management, Department of Mathematics, Plot No. 97, Sector 56, HSIIDC Industrial Estate, Kundli 131 028, Haryana, India
^b School of Advanced Sciences, Department of Mathematics, VIT University, Vellore 632 014, Tamil Nadu, India
^c Department of Mathematics, Jawaharlal Nehru Technological University, Hyderabad, Andhra Pradesh, India
^d Department of Mathematics, Aliah University, DN-41, Salt Lake, Sector V, Kolkata 700 091, India

Corresponding author.

Bienvenue sur EM-consulte, la référence des professionnels de santé.
L’accès au texte intégral de cet article nécessite un abonnement.

pages	11
Iconographies	5
Vidéos	0
Autres	0

Abstract

We consider a biological economic model based on prey–predator interactions to study the dynamical behaviour of a fishery resource system consisting of one prey and two predators surviving on the same prey. The mathematical model is a set of first order non-linear differential equations in three variables with the population densities of one prey and the two predators. All the possible equilibrium points of the model are identified, where the local and global stabilities are investigated. Biological and bionomical equilibriums of the system are also derived. We have analysed the population intensities of fluctuations i.e., variances around the positive equilibrium due to noise with incorporation of a constant delay leading to chaos, and lastly have investigated the stability and chaotic phenomena with a computer simulation.

Le texte complet de cet article est disponible en PDF.

Keywords : Prey–predator, Local and global stability, Bionomic equilibrium, Stochastic delayed perturbation, Fourier transform methods, Chaos