Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems

Details Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems

2011-11-11

arxiv.org/abs/1111.2773v1

Mathematics

Dynamical Systems

Scientific paper

We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly use the method of Darboux with extensions for inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable.

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