Estimation of the largest Lyapunov exponent-like LLEL stability measure parameter from the perturbation vector and its derivative dot product part 2 experiment simulationReport as inadecuate




Estimation of the largest Lyapunov exponent-like LLEL stability measure parameter from the perturbation vector and its derivative dot product part 2 experiment simulation - Download this document for free, or read online. Document in PDF available to download.

Nonlinear Dynamics

, Volume 78, Issue 3, pp 1601–1608

First Online: 01 July 2014Received: 20 September 2013Accepted: 11 June 2014

Abstract

Controlling system dynamics with use of the Largest Lyapunov Exponent LLE is employed in many different areas of the scientific research. Thus, there is still need to elaborate fast and simple methods of LLE calculation. This article is the second part of the one presented in Dabrowski Nonlinear Dyn 67:283–291, 2012. It develops method LLEDP of the LLE estimation and shows that from the time series of two identical systems, one can simply extract value of the stability parameter which value can be treated as largest LLE. Unlike the method presented in part, one developed method LLEDPT can be applied to the dynamical systems of any type, continuous, with discontinuities, with time delay and others. The theoretical improvement shows simplicity of the method and its obvious physical background. The proofs for the method effectiveness are based on results of the simulations of the experiments for Duffing and Van der Pole oscillators. These results were compared with ones obtained with use of the Stefanski method Stefanski in Chaos Soliton Fract 1115:2443–2451, 2000; Chaos Soliton Fract 15:233–244, 2003; Chaos Soliton Fract 23:1651–1659, 2005; J Theor Appl Mech 463:665–678, 2008 and LLEDP method. LLEDPT can be used also as the criterion of stability of the control system, where desired behavior of controlled system is explicitly known Balcerzak et al. in Mech Mech Eng 174:325–339, 2013. The next step of development of the method can be considered in direction that allows estimation of LLE from the real time series, systems with discontinuities, with time delay and others.

KeywordsStability Largest Lyapunov exponent Nonlinear dynamics  Download fulltext PDF



Author: Artur Dabrowski

Source: https://link.springer.com/







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