Article
Kyungpook Mathematical Journal 2017; 57(2): 265-285
Published online June 23, 2017
Copyright © Kyungpook Mathematical Journal.
Delayed Dynamics of Prey-Predator System with Distinct Functional Responses
V. Madhusudanan1
S. Vijaya2
Department of Mathematics, S.A. Engineering College, Chennai 600 072, Tamilnadu, India1
Department of Mathematics, Annamalai University, Annamalainagar 608 002, Tamilnadu, India2
Received: October 31, 2015; Accepted: January 24, 2017
In this article, a mathematical model is proposed and analyzed to study the delayed dynamics of a system having a predator and two preys with distinct growth rates and functional responses. The equilibrium points of proposed system are determined and the local stability at each of the possible equilibrium points is investigated by its corresponding characteristic equation. The boundedness of the system is established in the absence of delay and the condition for existence of persistence in the system is determined. The discrete type gestational delay of predator is also incorporated on the system. Further it is proved that the system undergoes Hopf bifurcation using delay as bifurcation parameter. This study refers that time delay may have an impact on the stability of the system. Finally Computer simulations illustrate the dynamics of the system.
Keywords: predator-prey system, growth rate, functional response, local stability, persistence, Hopf bifurcation, discrete delay