Flow curvature manifold and energy of generalized Liénard systems

Jean-Marc Ginoux, Dirk Lebiedz, Riccardo Meucci and Jaume Llibre

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

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 ε-vicinity of the slow invariant manifold of generalized Liénard systems, the curvature of trajectory curve increases while the energy of such systems decreases. Hence, we prove Minorsky's statement for the generalized Liénard systems. These results are then illustrated with the classical Van der Pol and generalized Liénard singularly perturbed systems.

Keywords: Generalized Liénard systems; Singularly perturbed systems; Flow Curvature Method (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005641

DOI: 10.1016/j.chaos.2022.112354

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