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Bifurcation analysis and chaos control in discrete-time eco–epidemiological models of pelicans at risk in the Salton Sea

  • Qamar DinEmail author
  • Waqas Ishaque
Article
  • 46 Downloads

Abstract

Parasites play vital role in dynamics of predator–prey interaction and regulating bio-diversity. We study qualitative behavior of two 3-dimensional discrete-time predator–prey-parasite models. Bifurcation analysis and chaos control are discussed by taking into account the study of an eco–epidemiological model of pelicans at risk in the Salton Sea. Discrete-time models are obtained with implementations of Euler’s forward scheme and piecewise constant argument for differential equations. Local asymptotic stability of equilibria is investigated, and explicit Hopf bifurcation and period-doubling bifurcation criteria are implemented to discuss emergence of both type of bifurcations at positive steady-states of discrete-time models. Moreover, some chaos control techniques are implemented for controlling chaotic behavior under the influence of bifurcations. Numerical simulations are provided to illustrate theoretical discussion.

Keywords

Predator–prey-parasite model Stability Neimark–Sacker bifurcation Period-doubling bifurcation Chaos control 

Mathematics Subject Classification

39A30 40A05 92D25 92C50 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PoonchRawalakotPakistan
  2. 2.Department of MathematicsUniversity of Azad Jammu and KashmirMuzaffarabadPakistan

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