Integrability and Linearizability of the Lotka–Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

By Simon Gravel, Pierre Thibault. 2002

50 citations recorded by the source corpus.

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∈ R + or λ∈ Q . These conditions will allow us to find all the integrable and linearizable systems for λ= p 2 and 2 p with p∈ N +.

Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/f7df64a4730b1e19742f2fb4f7c5014976abeca0

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In Geometry and Topology

1. Nicolae Vulpe
2. Dana Schlomiuk

Citations in the corpus

• Integrability and linearizability of the Lotka-Volterra systems (2004, unknown): “Keywords: Integrability; Linearizability; Lotka–Volterra system; Center problem”
• Global classification of the planar Lotka–Volterra differential systems according to their configurations of invariant straight lines (2010, background): “Local studies on normalizability, linearizability and integrability were done in [27], [28], [29], [39], [47].”