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Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities. (English) Zbl 1217.34058
Summary: 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 $x'=x(1-a_{30}x^3-a_{21}x^y-a_{12}xy^2-a_03y^3)$, $y'=-y(1-b_{30}x^3-b_{21}x^2y-b_{12}xy^2-b_{03}y^3$. 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.

34C20Transformation and reduction of ODE and systems, normal forms
34C05Location of integral curves, singular points, limit cycles (ODE)
37G05Normal forms
primdec; SINGULAR
Full Text: DOI
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