Stability of limit cycles in autonomous nonlinear systems

0426389 - ÚTAM 2015 RIV NL eng J - Journal Article
Náprstek, Jiří - Fischer, Cyril
Stability of limit cycles in autonomous nonlinear systems.
Meccanica. Roč. 49, č. 8 (2014), s. 1929-1943. ISSN 0025-6455. E-ISSN 1572-9648
R&D Projects: GA AV ČR(CZ) IAA200710902; GA ČR(CZ) GA103/09/0094; GA ČR(CZ) GC13-34405J
Institutional support: RVO:68378297
Keywords : limit cycle * nonlinear oscillator * stability
Subject RIV: JM - Building Engineering
Impact factor: 1.949, year: 2014
http://link.springer.com/article/10.1007/s11012-014-9899-8

Periodical solutions or limit cycles (LC) comprise a significant family among the response types of nonlinear autonomous systems. Their identification and stability assessment is of a great importance during the analysis of an unknown system. A new analytical/iterative method of LC identification and portrait investigation was presented recently. The current study proposes a novel technique for their stability assessment. This strategy facilitates the distinction of stable and unstable LCs, thereby allowing the definition of attractive and repulsive response fields. A narrow toroidal domain is constructed around the LC, which is arithmetized by an orthogonal system that is positioned by tangential and normal vectors to the LC. The stability of the LC is investigated using the transformed differential system of the normal components of the response, which are functions of the coordinate along the LC trajectory. Exponential LC stability criteria are also proposed, which are based on the first degree of the perturbation procedure. Theoretical considerations are illustrated using single and two degree of freedom systems including demonstrations with specific systems. The strengths, future steps, and shortcomings of this method are evaluated.
Permanent Link: http://hdl.handle.net/11104/0234151