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2005.13: Delay embedding in the presence of dynamical noise

2005.13: M. R. Muldoon, D. S. Broomhead, J. P. Huke and R. Hegger (1998) Delay embedding in the presence of dynamical noise. Dynamics and Stability of Systems, 13 (2). pp. 175-186. ISSN 0268-1110

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Abstract

We present a new embedding theorem for time series, in the spirit of Takens's theorem, but requiring multivariate signals. Our result is part of a growing body of work that extends the domain of geometric time series analysis to some genuinely stochastic systems---including such natural examples as

x_{j+1} = \phi(x_j) + \eta_j

where \phi is some fixed map and the \eta_j are i.i.d. random displacements.

Item Type:Article
Uncontrolled Keywords:chaos, delay embedding, noise
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2005.13
Deposited By:Dr Mark Muldoon
Deposited On:14 November 2005

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