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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 0 3y 3 ), y ' =-y(1-b 30 x 3 -b 21 x 2 y-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.
MSC:
34C20Transformation and reduction of ODE and systems, normal forms
34C05Location of integral curves, singular points, limit cycles (ODE)
37G05Normal forms
Software:
SINGULAR
References:
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