Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Delayed Dynamics of Prey-Predator System with Distinct Functional Responses

  • Madhusudanan, V. (Department of Mathematics, S.A. Engineering College) ;
  • Vijaya, S. (Department of Mathematics, Annamalai University)
  • Received : 2015.10.31
  • Accepted : 2017.01.24
  • Published : 2017.06.23
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Abstract

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.

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References

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