Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems
| Autor: | Elbert E. N. Macau, T. L. Prado, Fabiano A. S. Ferrari, G. Z. dos Santos Lima, Sergio Roberto Lopes, B. R. R. Boaretto, Gilberto Corso, R. C. Budzinski |
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| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Principle of maximum entropy General Physics and Astronomy Statistical and Nonlinear Physics Lyapunov exponent 01 natural sciences 010305 fluids & plasmas Nonlinear dynamical systems symbols.namesake Chaotic systems 0103 physical sciences Poincaré conjecture symbols Applied mathematics 010306 general physics Recurrence plot Mathematical Physics Mathematics |
| Zdroj: | Chaos (Woodbury, N.Y.). 30(4) |
| ISSN: | 1089-7682 |
| Popis: | The recurrence analysis of dynamic systems has been studied since Poincare’s seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy ( S max). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood ( ϵ—vicinity), turning the analysis free of the vicinity parameter. In addition, ϵ turns out to be a novel quantifier of dynamical properties itself. We apply S max and the optimum ϵ to deterministic and stochastic systems. The S max quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series. |
| Databáze: | OpenAIRE |
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