A prey - partially dependent predator with a reserved zone: modelling and analysis

  • Authors

    • M.V. Ramana Murthy Departments of Mathematics, College of Science, Osmania University, Hyderabad, India
    • Dahlia Khaled Departments of Mathematics, College of Science, Osmania University, Hyderabad, India
    2015-12-17
    https://doi.org/10.14419/ijamr.v5i1.5238
  • Local Bifurcation, Prey-Predator, Persistent, Reserved Zone, Stability.

  • Abstract

    In this paper, a mathematical model consisting of a prey-partially dependent predator has been proposed and analyzed. It is assumed that the prey moving between two types of zones, one is assumed to be a free hunting zone that is known as an unreserved zone and the other is a reserved zone where hunting is prohibited. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. Finally, numerical simulation has been used to specify the control parameters and confirm the obtained results.

  • References

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  • How to Cite

    Murthy, M. R., & Khaled, D. (2015). A prey - partially dependent predator with a reserved zone: modelling and analysis. International Journal of Applied Mathematical Research, 5(1), 1-10. https://doi.org/10.14419/ijamr.v5i1.5238

    Received date: 2015-08-26

    Accepted date: 2015-12-08

    Published date: 2015-12-17