Flow curvature manifold and energy of generalized Lienard systems

Year: 2022

Authors: Ginoux JM., Lebiedz D., Meucci R., Llibre J.

Autors Affiliation: Univ Toulon & Var, Aix Marseille Univ, CNRS, CPT, Marseille, France; Inst Numer Math, Ulm, Germany; Ist Nazl Ottica, Florence, Italy; Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain.

Abstract: In his famous book entitled Theory of Oscillations, Nicolas Minorsky wrote: each time the system absorbs energy the curvature of its trajectory decreases and vice versa. By using the Flow Curvature Method, we establish that, in the epsilon-vicinity of the slow invariant manifold of generalized Lienard systems, the curvature of trajectory curve increases while the energy of such systems decreases. Hence, we prove Minorsky’s statement for the generalized Lienard systems. These results are then illustrated with the classical Van der Pol and generalized Lienard singularly perturbed systems.(c) 2022 Elsevier Ltd. All rights reserved.(c) 2022 Elsevier Ltd. All rights reserved.

Journal/Review: CHAOS SOLITONS & FRACTALS

Volume: 161      Pages from: 112354-1  to: 112354-7

More Information: The datasets generated during and analysed during the current study are available from the corresponding author on reasonable request. The second author (Dirk Lebiedz) is supported by the Klaus-Tschira Foundation (Germany) , grant 00.003.2019. The last author (Jaume Llibre) is partially supported the Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion grants MTM2016-77278-P (FEDER) and PID2019-104658GB-I00 (FEDER) , the Agencia de Gestio d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.
KeyWords: Generalized Li´nard systems; Singularly perturbed systems; Flow Curvature Method
DOI: 10.1016/j.chaos.2022.112354

ImpactFactor: 7.800
Citations: 3
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