Integrability and linearizability of the Lotka-Volterra system with a saddle point with rational hyperbolicity ratio

Abstract

In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and -λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ ε ℝ+ or λ ε ℚ. These conditions will allow us to find all the integrable and linearizable systems for λ = p/2 and 2/p, with p ε ℕ+. © 2002 Elsevier Science (USA).