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HOPF BIFURCATION INDUCED BY NEUTRAL DELAY IN A PREDATOR–PREY SYSTEM

BEN NIU

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China

Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China

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and

WEIHUA JIANG

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China

Author for correspondence.

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https://doi.org/10.1142/S0218127413501745Cited by:4 (Source: Crossref)

Abstract

A predator–prey system with neutral delay is investigated from the viewpoint of bifurcation analysis on neutral delay differential equations. Stability and Hopf bifurcation of the inner equilibrium are given, by which we show how the neutral terms affect the dynamical behavior of the prey and the predator. To give more detailed information on the periodic oscillations, the direction and stability of Hopf bifurcation are studied by using the normal form theory of neutral equation. We find neutral delay makes the predator–prey system more complicated and usually induces stability switches or double Hopf bifurcations. Near the double Hopf bifurcation we give the detailed bifurcation set by calculating the universal unfoldings. It is shown that the population of prey or predator may exhibit transient quasiperiodic oscillations driven by the neutral delay. Finally, we carry out several groups of illustrations.

Supported by NSFC (No. 11301117 and No. 11371112).

Keywords:

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