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
Computational and Applied Mathematics – Springer Journals
Published: Jun 5, 2018
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