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Received Nov 28, 2017; Revised Jan 12, 2018; Accepted Jan 28, 2018
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1. Introduction
One of the most applied techniques to confirm whether a system is chaotic or not is based on the estimation of the Lyapunov exponents [1]. The calculation of Lyapunov exponents is usually based on the average divergence or convergence of close trajectories along certain directions in state space. In chaotic systems, two trajectories separate exponentially with time despite having very similar initial conditions. Since the work of [2] several numerical methods to estimate Lyapunov exponents were proposed [3–8], just to mention a few. A comparison between estimation methods can be found in [9], for instance. The authors in [5] developed the first practical algorithm to calculate the Lyapunov exponents by estimating the growth of the corresponding set of vectors as the system evolves. This method allows the estimation of the complete spectrum of Lyapunov exponents. Amongst these exponents, the (positive) largest Lyapunov exponent (LLE) is the exponent considered to be the main reason for the separation rate. Therefore the estimation of such an exponent is used to build up the chaotic nature of the data under scrutiny. The authors in [1, 7] independently used statistical properties of the local divergence rates of nearby trajectories of the systems under investigation to estimate the LLE. These properties come in handy when the goal is to get high exactness of numerical estimates of the LLE, as shown in the work [10]. Recent and different applications using the LLE can be found in [11–14].
In [15] a straightforward method to compute the LLE using interval extensions and the original equations of motion was proposed. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system [16, 17]. The authors of [15] demonstrated that the method is quick and simple to be used and could be considered as an alternative to other algorithms available in the literature. However, it requires the original equations of motion of the system and it can not...