Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities

Jaume Giné; Zhibek Kadyrsizova; Yirong Liu; Valery G. Romanovski

doi:10.1016/j.camwa.2010.12.069

Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities

Jaume Giné, Zhibek Kadyrsizova, Yirong Liu, Valery G. Romanovski

Department of Mathematics

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

15 Citations (Scopus)

Abstract

In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a₃₀x³-a₂₁x²y-a ₁₂xy²-a₀₃y³), y=-y(1-b ₃₀x³-b₂₁x²y-b₁₂xy ²-b₀₃y³). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.

Original language	English
Pages (from-to)	1190-1201
Number of pages	12
Journal	Computers and Mathematics with Applications
Volume	61
Issue number	4
DOIs	https://doi.org/10.1016/j.camwa.2010.12.069
Publication status	Published - Feb 2011

Keywords

Isochronicity
Linearizability
Polynomial differential system
Polynomial vector field

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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title = "Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities",

abstract = "In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a30x3-a21x2y-a 12xy2-a03y3), y=-y(1-b 30x3-b21x2y-b12xy 2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.",

keywords = "Isochronicity, Linearizability, Polynomial differential system, Polynomial vector field",

author = "Jaume Gin{\'e} and Zhibek Kadyrsizova and Yirong Liu and Romanovski, {Valery G.}",

note = "Funding Information: The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first author is partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2009SGR 381 . The third author is partially supported by the National Natural Science Foundation of China ( 10771196 ). The fourth author is supported by the Slovenian Research Agency , by the Nova Kreditna Banka Maribor , by TELEKOM Slovenije , and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133 ).",

year = "2011",

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doi = "10.1016/j.camwa.2010.12.069",

language = "English",

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pages = "1190--1201",

journal = "Computers and Mathematics with Applications",

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AU - Giné, Jaume

AU - Kadyrsizova, Zhibek

AU - Liu, Yirong

AU - Romanovski, Valery G.

N1 - Funding Information: The authors are grateful to the referees for their valuable remarks which helped to improve the manuscript. The first author is partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2009SGR 381 . The third author is partially supported by the National Natural Science Foundation of China ( 10771196 ). The fourth author is supported by the Slovenian Research Agency , by the Nova Kreditna Banka Maribor , by TELEKOM Slovenije , and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133 ).

PY - 2011/2

Y1 - 2011/2

N2 - In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a30x3-a21x2y-a 12xy2-a03y3), y=-y(1-b 30x3-b21x2y-b12xy 2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.

AB - In this paper we investigate the linearizability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, i.e., we consider systems of the form x=x(1-a30x3-a21x2y-a 12xy2-a03y3), y=-y(1-b 30x3-b21x2y-b12xy 2-b03y3). The necessary and sufficient conditions for the linearizability of this system are found. From them the conditions for isochronicity of the corresponding real system can be derived.

KW - Isochronicity

KW - Linearizability

KW - Polynomial differential system

KW - Polynomial vector field

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