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

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

Research output: Contribution to journalArticle

13 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 languageEnglish
Pages (from-to)1190-1201
Number of pages12
JournalComputers and Mathematics with Applications
Volume61
Issue number4
DOIs
Publication statusPublished - Feb 2011
Externally publishedYes

Fingerprint

Linearizability
Lotka-Volterra
Control nonlinearities
Quartic
Linear systems
Large scale systems
Polynomials
Nonlinearity
Homogeneous Polynomials
Linear Systems
Necessary Conditions
Sufficient Conditions

Keywords

  • Isochronicity
  • Linearizability
  • Polynomial differential system
  • Polynomial vector field

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities. / Giné, Jaume; Kadyrsizova, Zhibek; Liu, Yirong; Romanovski, Valery G.

In: Computers and Mathematics with Applications, Vol. 61, No. 4, 02.2011, p. 1190-1201.

Research output: Contribution to journalArticle

Giné, Jaume ; Kadyrsizova, Zhibek ; Liu, Yirong ; Romanovski, Valery G. / Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities. In: Computers and Mathematics with Applications. 2011 ; Vol. 61, No. 4. pp. 1190-1201.
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