Energy function of 2D and 3D coarse systems
Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon)
Meucci, Riccardo (Centre National de la Recherche Scientifique. Université de Toulon)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Sprott, Julien Clinton (University of Wisconsin)

Date:	2025
Abstract:	In this work, while using the Flow Curvature Method developed by one of us (JMG), we prove that the energy function of two and three-dimensional coarse systems involving a small parameter μ can be directly deduced from the curvature of their trajectory curves when μ tends to zero. Such a result thus confirms the relationship between curvature and energy function for a certain class of differential systems already established in one of our previous contributions. Then, we state that the rate of change of the energy function of such coarse systems is equal to the scalar product of the velocity vector field and its first time derivative, i. e. the acceleration vector field. The comparison of these results with the so-called Frénet frame enables to prove that energy function is proportional to the normal component of the acceleration when μ tends to zero while the rate of change of the energy function is proportional to the tangential component of the acceleration at first order in μ. Two and three-dimensional examples are then used to emphasize these two main results.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Energy function ; Coarse systems ; Zero-Hopf bifurcation ; Van der Pol system ; Li-Sprott model
Published in:	Chaos, solitons and fractals, Vol. 199, Part 1 (October 2025) , art. 116643, ISSN 0960-0779

DOI: 10.1016/j.chaos.2025.116643

9 p, 2.5 MB

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