On the Darboux integrability of the Hindmarsh-Rose burster
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

Date:	2018
Abstract:	We study the Hindmarsh–Rose burster which can be described by the differential system x?=y?x3+bx2+I?z,y?=1?5x2?y,z?=?(s(x?x0)?z), where b, I, ?, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial integrability ; Rational integrability ; Darboux polynomials ; Darboux first integrals ; Invariant algebraic surfaces ; Exponential factors ; Hindmarsh-Rose burster
Published in:	Acta Mathematica Sinica. English Series, Vol. 34, issue 6 (2018) , p. 947-958, ISSN 1439-7617

DOI: 10.1007/s10114-017-5661-1

Postprint 13 p, 731.7 KB

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