Zero-hopf bifurcation in the volterra-gause system of predator-prey type

Jean Marc Ginoux; Jaume Llibre

doi:10.1002/mma.4569

Zero-hopf bifurcation in the volterra-gause system of predator-prey type

Jean Marc Ginoux, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

© 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.

Original language	English
Pages (from-to)	7858-7866
Journal	Mathematical Methods in the Applied Sciences
Volume	40
Issue number	18
DOIs	https://doi.org/10.1002/mma.4569
Publication status	Published - 1 Dec 2017

Keywords

Periodic orbits
Predator-prey system
Volterra-Gause system
Zero-Hopf bifurcation

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title = "Zero-hopf bifurcation in the volterra-gause system of predator-prey type",

abstract = "{\textcopyright} 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.",

keywords = "Periodic orbits, Predator-prey system, Volterra-Gause system, Zero-Hopf bifurcation",

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T1 - Zero-hopf bifurcation in the volterra-gause system of predator-prey type

AU - Ginoux, Jean Marc

AU - Llibre, Jaume

PY - 2017/12/1

Y1 - 2017/12/1

N2 - © 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.

AB - © 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.

KW - Periodic orbits

KW - Predator-prey system

KW - Volterra-Gause system

KW - Zero-Hopf bifurcation

U2 - 10.1002/mma.4569

DO - 10.1002/mma.4569

M3 - Article

VL - 40

SP - 7858

EP - 7866

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 18

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