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

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

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13 Citations (Scopus)


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
Issue number4
Publication statusPublished - Feb 1 2011



  • 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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