| Full text | |
| Author(s): |
Fazanaro, Filipe I.
[1]
;
Soriano, Diogo C.
[2]
;
Suyama, Ricardo
[2]
;
Attux, Romis
[1]
;
Madrid, Marconi K.
[3]
;
De Oliveira, Jose Raimundo
[1]
Total Authors: 6
|
| Affiliation: | [1] Univ Estadual Campinas, Sch Elect & Comp Engn FEEC, Dept Comp Engn & Ind Automat DCA, BR-13083852 Campinas, SP - Brazil
[2] Univ Fed ABC UFABC, Ctr Engn Modelagem & Ciencias Sociais Aplicadas, Santo Andre - Brazil
[3] Univ Estadual Campinas, FEEC, Dept Energy & Syst DSCE, BR-13083852 Campinas, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Chaos; v. 23, n. 2 JUN 2013. |
| Web of Science Citations: | 5 |
| Abstract | |
The present work aims to apply a recently proposed method for estimating Lyapunov exponents to characterize-with the aid of the metric entropy and the fractal dimension-the degree of information and the topological structure associated with multiscroll attractors. In particular, the employed methodology offers the possibility of obtaining the whole Lyapunov spectrum directly from the state equations without employing any linearization procedure or time series-based analysis. As a main result, the predictability and the complexity associated with the phase trajectory were quantified as the number of scrolls are progressively increased for a particular piecewise linear model. In general, it is shown here that the trajectory tends to increase its complexity and unpredictability following an exponential behaviour with the addition of scrolls towards to an upper bound limit, except for some degenerated situations where a non-uniform grid of scrolls is attained. Moreover, the approach employed here also provides an easy way for estimating the finite time Lyapunov exponents of the dynamics and, consequently, the Lagrangian coherent structures for the vector field. These structures are particularly important to understand the stretching/folding behaviour underlying the chaotic multiscroll structure and can provide a better insight of phase space partition and exploration as new scrolls are progressively added to the attractor. (C) 2013 AIP Publishing LLC (AU) | |
| FAPESP's process: | 12/09624-4 - Information Processing Using Multiscroll Attractors: Theoretical and Practical Aspects |
| Grantee: | Filipe Ieda Fazanaro |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |