The Hopf bifurcation and stability of delayed predator–prey system

The Hopf bifurcation and stability of delayed predator–prey system Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0658-7 The Hopf bifurcation and stability of delayed predator–prey system 1 1 Meriem Bentounsi · Imane Agmour · 1 1,2 Naceur Achtaich · Youssef El Foutayeni Received: 14 January 2018 / Revised: 5 May 2018 / Accepted: 29 May 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract In this paper, a mathematical model consisting of three populations with discrete time delays is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are analyzed using the theory of normal form and center manifold. Discussion with some numerical simulation examples is given to support the theoretical results. Keywords Predator–prey · Stability analysis · Hopf bifurcation · Discrete delay Mathematics Subject Classification 91B05 · 91A06 · 91B02 · 91B50 1 Introduction Over the last decade, the dynamic behavior of predator–prey systems has received much attention from many applied mathematicians and ecologists. Many theoreticians and experi- Communicated by Maria do Rosário de Pinho. B Youssef El Foutayeni http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

The Hopf bifurcation and stability of delayed predator–prey system

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Publisher
Springer Journals
Copyright
Copyright © 2018 by SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-018-0658-7
Publisher site
See Article on Publisher Site

Abstract

Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0658-7 The Hopf bifurcation and stability of delayed predator–prey system 1 1 Meriem Bentounsi · Imane Agmour · 1 1,2 Naceur Achtaich · Youssef El Foutayeni Received: 14 January 2018 / Revised: 5 May 2018 / Accepted: 29 May 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract In this paper, a mathematical model consisting of three populations with discrete time delays is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are analyzed using the theory of normal form and center manifold. Discussion with some numerical simulation examples is given to support the theoretical results. Keywords Predator–prey · Stability analysis · Hopf bifurcation · Discrete delay Mathematics Subject Classification 91B05 · 91A06 · 91B02 · 91B50 1 Introduction Over the last decade, the dynamic behavior of predator–prey systems has received much attention from many applied mathematicians and ecologists. Many theoreticians and experi- Communicated by Maria do Rosário de Pinho. B Youssef El Foutayeni

Journal

Computational and Applied MathematicsSpringer Journals

Published: Jun 5, 2018

References

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