Integrability Conditions for Lotka-Volterra Planar Complex Quartic Systems Having Homogeneous Nonlinearities

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 [email protected]?=x(1-a"3"0x^3-a"2"1x^2y-a"1"2xy^2-a"0"3y^3), [email protected]?=-y(1-b"3"0x^3-b"2"1x^2y-b"1"2xy^2-b"0"3y^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.

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