Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test

Abstract

Shape memory oscillators are thermomechanical hysteretic systems that, in a wide range of model parameters, can exhibit complex non-periodic non-linear dynamic responses under the excitation of a periodic force. In this study, the statistical 0-1 test based on the asymptotic properties of a Brownian motion chain is applied to periodic and nonperiodic isothermal trajectories to examine the type of motion. The analysis is based on the computation of the control parameter K that approaches asymptotically 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent of the integration procedure, being based on the characteristic sampling distance between the points of the analysed time series. The numerical results show that the test is able to unambiguously distinguish periodic from chaotic trajectories.

A Modified 0-1 Test for Chaos Detection in Oversampled Time Series Observations

“…This result suggests that although any type of map can be used for detecting chaos, the map of local maxima and minima minimizes the false detections as compared to other mapping techniques. Such a map was already used in the 0-1 test for a dynamical system with a shape memory device including hysteresis [Bernardini et al, 2013]. The present work thus confirms that the choice of the map of local maxima and minima is a promising method for well known dynamical systems.…”

“…The reliability of this method has been established and successfully proven in various deterministic systems [Hu et al, 2005;Gottwald & Melbourne, 2009b;Zachilas & Psarianos, 2012]. Recently, the 0-1 test method has been used to detect chaos in a regenerative cutting process with memory, the dynamical system with a shape memory device [Litak et al, 2009a;Bernardini et al, 2013]. Standard approaches based on Lyapunov exponent method fail to detect chaos in a dynamical nonsmooth system with hysteresis, so the 0-1 test was used to detect chaos in such a system [Litak et al, 2009b;Litak et al, 2012Litak et al, , 2009a.…”

Characterizing the nonlinear behavior of a pseudoelastic oscillator via the wavelet transform

“…12 As shown in Litak et al, 11 the 0-1 test has been used successfully to analyze the nonisothermal nonlinear response of pseudoelastic oscillators. Basically, the 0-1 test consists of estimating a single parameter "…”

Recurrence analysis of regular and chaotic motions of a superelastic shape memory oscillator

“…Due to the hysteretic behaviour induced by the non-smoothness of underlying differential equations, the most typical tool for chaos diagnosis, namely Lyapunov exponents, is difficult to employed. Therefore, various, alternative diagnostic methods have been proposed, as for example, 0-1 test [12,13] and the method of wandering trajectories [10,11].…”