Hopf bifurcation of a generalized Moon-Rand system

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1016/j.cnsns.2014.06.041

Hopf bifurcation of a generalized Moon-Rand system

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

4 Citations (Scopus)

Abstract

© 2014 Elsevier B.V. We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon-Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.

Original language	English
Pages (from-to)	1070-1077
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	20
Issue number	3
DOIs	https://doi.org/10.1016/j.cnsns.2014.06.041
Publication status	Published - 1 Jan 2015

Keywords

Averaging theory
Hopf bifurcation
Moon-Rand systems

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https://doi.org/10.1016/j.cnsns.2014.06.041

https://ddd.uab.cat/record/145339

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title = "Hopf bifurcation of a generalized Moon-Rand system",

abstract = "{\textcopyright} 2014 Elsevier B.V. We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon-Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.",

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T1 - Hopf bifurcation of a generalized Moon-Rand system

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2015/1/1

Y1 - 2015/1/1

N2 - © 2014 Elsevier B.V. We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon-Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.

AB - © 2014 Elsevier B.V. We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon-Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.

KW - Averaging theory

KW - Hopf bifurcation

KW - Moon-Rand systems

U2 - https://doi.org/10.1016/j.cnsns.2014.06.041

DO - https://doi.org/10.1016/j.cnsns.2014.06.041

M3 - Article

SN - 1007-5704

VL - 20

SP - 1070

EP - 1077

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 3

ER -

Hopf bifurcation of a generalized Moon-Rand system

Abstract

Keywords

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