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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:184

Article

Gravel, S ; Thibault, P

关键词: Lotka-Volterra system;    linearizability;    integrability;    normalizability;   

DOI  :  10.1006/jdeq.2001.4128

来源: Elsevier

【 摘 要 】

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 lambda. 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 lambda is an element of R or lambda is an element of Q. These conditions will allow us to find all the integrable and linearizable systems for and with rho is an element of N+. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free