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Dynamical study of a chaotic predator-prey model with an omnivore

  • A. Al-khedhairi
  • A. A. ElsadanyEmail author
  • A. Elsonbaty
  • A. G. Abdelwahab
Regular Article

Abstract.

In this paper, the dynamics and bifurcations of a three-species predator-prey model with an omnivore are further investigated. The food web considered in this work comprises prey, predator and a third species, which consumes the carcasses of the predator along with predation of the original prey. The conditions for existence, uniqueness and continuous dependence on initial conditions for the solution of the model are derived. Analytical and numerical bifurcation studies reveal that the system undergoes transcritical and Hopf bifurcations around its equilibrium points. Further, the Hopf bifurcation curves in the parameters’ space along with codimension two bifurcations of equilibrium points and bifurcation of limit cycles that arise in the system are investigated. In particular, the occurrence of generalized Hopf, fold Hopf and Neimarck-Sacker bifurcations is unveiled and illustrates the rich dynamics of the model. Finally, bifurcation diagrams, phase portraits and Lyapunov exponents of the model are presented.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • A. Al-khedhairi
    • 1
  • A. A. Elsadany
    • 2
    Email author
  • A. Elsonbaty
    • 3
  • A. G. Abdelwahab
    • 2
  1. 1.Department of Statistics and Operations Researches, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Department of Basic Science, Faculty of Computers and InformaticsSuez Canal UniversityIsmailiaEgypt
  3. 3.Department of Mathematics and Engineering Physics, Faculty of EngineeringMansoura UniversityMansouraEgypt

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