Dynamics of a class of 3-dimensional Lotka-Volterra Systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2023
Abstract:	We provide the complete dynamics of the Lotka-Volterra differential system x˙ = x(ay − cz), y˙ = y(bz − ax), z˙ = z(cx − by), where a, b, c are positive parameters and x, y, z are in the positive octant of R3. In particular we show that this system is completely integrable, i. e. it has two independent first integrals. Fixing one of these first integrals we obtain invariant triangles in the positive octant of R3. The dynamics of the system on each one of these invariant triangles is given by an equilibrium point surrounded by periodic orbits, i. e. by a center. In short all the orbits of these system are either equilibrium points, or periodic orbits. This nonlinear differential system models, under the conservation of mass, a cycle ofirreversible autocatalytic reactions between the different states of three macromolecules and allows to describe stable chemical oscillations.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Lotka-Volterra system ; Invariant ; Global dynamics ; Phase portrait
Published in:	Dynamics of continuous, discrete and impulsive systems, Vol. 30, Issue 4 (2023) , p. 303-307, ISSN 1918-2538

Adreça alternativa: https://online.watsci.org/abstract_pdf/2023v30/v30n4a-pdf/4.pdf

Postprint 6 p, 248.5 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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