Bifurcation Analysis of a Multi-Parameter Liénard Polynomial System

Valery Gaiko; Cornelis Vuik; Huibert A.J. Reijm

doi:10.1016/j.ifacol.2018.12.108

Bifurcation Analysis of a Multi-Parameter Liénard Polynomial System

Valery Gaiko, Cornelis Vuik, Huibert A.J. Reijm

Numerical Analysis

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Abstract

In this paper, we study a multi-parameter Liénard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the application of a canonical system with field rotation parameters. Using this method, we present a solution of Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the Liénard polynomial system. We also conduct some numerical experiments to illustrate the obtained results.

Original language	English
Pages (from-to)	144-149
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	51
Issue number	33
DOIs	https://doi.org/10.1016/j.ifacol.2018.12.108
Publication status	Published - 2018

Keywords

field rotation parameter
global bifurcation analysis
limit cycle
multi-parameter Liénard polynomial system

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10.1016/j.ifacol.2018.12.108

49462958 - 1-s2.0-S2405896318336516-mainFinal published version, 437 KB

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title = "Bifurcation Analysis of a Multi-Parameter Li{\'e}nard Polynomial System",

abstract = "In this paper, we study a multi-parameter Li{\'e}nard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the application of a canonical system with field rotation parameters. Using this method, we present a solution of Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the Li{\'e}nard polynomial system. We also conduct some numerical experiments to illustrate the obtained results.",

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AU - Gaiko, Valery

AU - Vuik, Cornelis

AU - Reijm, Huibert A.J.

PY - 2018

Y1 - 2018

N2 - In this paper, we study a multi-parameter Liénard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the application of a canonical system with field rotation parameters. Using this method, we present a solution of Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the Liénard polynomial system. We also conduct some numerical experiments to illustrate the obtained results.

AB - In this paper, we study a multi-parameter Liénard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our bifurcational geometric method based on the application of a canonical system with field rotation parameters. Using this method, we present a solution of Hilbert's Sixteenth Problem on the maximum number of limit cycles and their distribution for the Liénard polynomial system. We also conduct some numerical experiments to illustrate the obtained results.

KW - field rotation parameter

KW - global bifurcation analysis

KW - limit cycle

KW - multi-parameter Liénard polynomial system

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DO - 10.1016/j.ifacol.2018.12.108

M3 - Conference article

AN - SCOPUS:85059120729

SN - 2405-8963

VL - 51

SP - 144

EP - 149

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 33

ER -

Bifurcation Analysis of a Multi-Parameter Liénard Polynomial System

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