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Darboux first integral conditions and integrability of the 3D Lotka-Volterra system

Laurent Cairó
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Abstract

We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3-dimensional Lotka-Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases of integrability.

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Laurent Cairó. 2000-10-01. Darboux first integral conditions and integrability of the 3D Lotka-Volterra system. https://doi.org/10.2991/jnmp.2000.7.4.7

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