Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been growing. Thus, at this moment, in MathSciNet there are 108 articles with the words rigid systems or uniform systems in their titles. Here, we study the dynamics of the planar rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree. More precisely, we characterize the existence and non-existence of limit cycles in this class of rigid systems, and we determine the local phase portraits of their finite and infinite equilibrium points in the Poincaré disc. Finally, we classify the global phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearities that can exhibit one limit cycle.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
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:	Quadratic systems ; Quadratic differential systems ; Limit cycles ; Rigid system ; Rigid differential systems
Published in:	Mathematics, Vol. 12, Issue 18 (September 2024) , art. 2806, ISSN 2227-7390

DOI: 10.3390/math12182806

10 p, 703.2 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
Articles > Published articles