Abstract
We present a method for the detection of periodic motions in long-time series of data. In contrast to other commonly used approaches, e.g., empirical orthogonal functions, principal oscillation patterns, singular spectrum analyses, this method is oriented towards scalar-quantities, therefore, it does not require the introduction of an arbitrary metric in the space of the dynamical variables. Nonlinear effects are included; needless to say, the higher the non-linearities included the longer and more complicated the actual calculations become. We are trying the method on a Lorenz model and on a simple model of the dynamics of the atmosphere.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kendall B.E., Schaffer W.M. and Tidd C.W. (1993), ‘Transient periodicity in chaos’, Phys. Lett. A, 117, 13–20.
Ruelle D. (1978), ‘Statistical Mechanics, Thermodynamic Formalism’, Addison-Wesley
Reading MA, (1986), ‘Resonances of chaotic dynamical systems’, Phys. Rev. Letters, 56, 405
Reading MA, (1986), ‘Locating resonances for axiom A dynamical systems’, J. Statist. Phys., 44, 281.
Cvitanović P. (1988), ‘Invariant measurement of strange sets in terms of cycles’, Phys. Rev. Letters, 61, 2729;
Artuso R., Aurell E. and Cvitanović P. (1990), ‘Recycling of strange sets: I (Cycle expansions) and II (Applications)’, Nonlinearity, 3, 325–359 and 360–386;
Cvitanović P., Gaspard P. and Schreiber T. (1992), ‘Investigation of the Lorentz gas in terms of periodic orbits’, Chaos, 2, 85.
Auerbach D., Cvitanović P., Eckmann J.-P., Gunaratne G.H. and Procaccia I. (1987), Phys. Rev. Letters, 58, 23–87;
Biham O. and Wenzel W. (1989), ‘Characterization of unstable periodic orbits in chaotic attractors and repellers’, Phys. Rev. Letters, 63, 819.
Loéve M.M. (1955), ‘Probability Theory’, van Nostrand, Princeton, NJ;
Lumley J.L. (1970), ‘Stochastic Tools in Turbulence’, Academic Press, N.Y.
Hasselmann K. (1988), ‘PIPs and POPs–A general formalism for the reduction of dynamical systems in terms of Principal Interaction Patterns and Principal Oscillation Patterns’, J. Geophys. Res., 93, 11015–11021.
R.A. Pasmanter, to be published.
Lorenz E.N. (1984), ‘Irregularity: a fundamental property of the atmosphere’, Tellus, 36 A, 98.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Pasmanter, R.A. (1994). Searching for Periodic Motions in Long-Time Series. In: Grasman, J., van Straten, G. (eds) Predictability and Nonlinear Modelling in Natural Sciences and Economics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0962-8_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-0962-8_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4416-5
Online ISBN: 978-94-011-0962-8
eBook Packages: Springer Book Archive