Attractor reconstruction from filtered chaotic time series

Chennaoui, A.; Pawelzik, Klaus; Liebert, Wolfgang; Schuster, H. G.; Pfister, G.

doi:10.1103/physreva.41.4151

Cited by 36 publications

(17 citation statements)

References 11 publications

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“…Many filters can be represented as a convolution of the chaotic signal s ( n ) with some kernel h (n) so that the actual measurement is (132) The question of what happens to the properties of the signal under this filtering has been addressed in many places (Sakai and Tokumaru, 1980;Mitschke et al , 1988;Chennaoui et al , 1990;Isabelle et al , 1991) with the following basic results. If the filter is a so-called moving-average or finite-impulse-response (FIR) filter, that is, a kernel of the form rather well understood.…”

Section: Lineari Y Filtered Signalsmentioning

confidence: 99%

The analysis of observed chaotic data in physical systems

et al. 1993

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Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical importance from such measurements.They discuss methods for (1) separating the signal of physical interest from contamination ("noise reduction"), (2) constructing an appropriate state space or phase space for the data in which the full structure of the strange attractor associated with the chaotic observations is unfolded, (3) evaluating invariant properties of the dynamics such as dimensions, Lyapunov exponents, and topological characteristics, and (4) model making, local and global, for prediction and other goals. They briefly touch on the efFects of linearly filtering data before analyzing it as a chaotic time series. Controlling chaotic physical systems and using them to synchronize and possibly communicate between source and receiver is considered. Finally, chaos in space-time systems, that is, the dynamics of fields, is briefly considered. %hile much is now known about the analysis of observed temporal chaos, spatio-temporal chaotic systems pose new challenges. The emphasis throughout the review is on the tools one now has for the realistic study of measured data in laboratory and field settings. It is the goal of this review to bring these tools into general use among physicists who study classical and semiclassical systems. Much of the progress in studying chaotic systems has rested on computational tools with some underlying rigorous mathematics. Heuristic and intuitive analysis tools guided by this mathematics and realizable on existing computers constitute the core of this review.

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Section: Lineari Y Filtered Signalsmentioning

confidence: 99%

The analysis of observed chaotic data in physical systems

et al. 1993

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“…Indeed, in the work of Chennaoui et al(1990), for example, a low-pass filter was used for the dynamic time series, particularly, from a logistic equation. In this case, the fractal dimension of the filtered time series of course increases.…”

Section: The Reconstruction Of the Fokker-planck Equation For The Mulmentioning

confidence: 99%

Optimization and Control of Bilinear Systems

Panos

Vitaliy

2008

Springer Optimization and Its Applications

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Aims and ScopeOptimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences.The series Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.

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“…In fact, depending upon the size of il compared to the other Lyapunov exponents, DL can increase as much as 1. There has been some work (e.g., Chennaoui et al, 1990) to remove this effect of filtering on chaotic time series by (at least in a topological sense) unfiltering the time series.…”

Section: The Effect Of Filtering the Observationsmentioning

confidence: 99%

Statistical Methods in Physical Oceanography: Proceedings of 'Aha Huliko'a Hawaiian Winter Workshop Held in Manoa, Hawaii on January 12-15, 1993

Müller¹,

Henderson²

1993

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Attractor reconstruction from filtered chaotic time series

Cited by 36 publications

References 11 publications

The analysis of observed chaotic data in physical systems

The analysis of observed chaotic data in physical systems

Optimization and Control of Bilinear Systems

Statistical Methods in Physical Oceanography: Proceedings of 'Aha Huliko'a Hawaiian Winter Workshop Held in Manoa, Hawaii on January 12-15, 1993

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