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

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 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 1 2011

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Keywords

Isochronicity
Linearizability
Polynomial differential system
Polynomial vector field

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Cite this

Giné, J., Kadyrsizova, Z., Liu, Y., & Romanovski, V. G. (2011). Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities. Computers and Mathematics with Applications, 61(4), 1190-1201. https://doi.org/10.1016/j.camwa.2010.12.069

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10.1016/j.camwa.2010.12.069