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On the use of the generalised entropy of curves to evaluate chaotic behaviours

Emanuele Crisostomi, Aldo Balestrino, Andrea Caiti
An Entropy of Curves based Indicator (ECI) is used here to evaluate and compare chaotic dynamical systems. ECI is computed according to a methodology that similarly to Monte Carlo calculations starts from an initial population of points in the state space. Each point evolves in time according to the equations of the underlying dynamical system and the generalised entropy of the curve connecting sequentially all the points is computed at each time step (ECI). According to such indicator all dynamical systems are characterised by a zero constant ECI, while higher values of the ECI indicate that the dynamical system is characterised by some nonlinearities. This paper is devoted to the analysis of chaotic systems, and computations of ECI in the case of well known chaotic systems are described and compared.
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