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Takens' Embedding Theorem forms the basis of virtually all approaches to the analysis of time series generated by nonlinear deterministic dynamical systems. It typically allows us to reconstruct an unknown dynamical system which gave rise to a given observed scalar time series simply by constructing a new state space out of successive values of the time… (More)

An approach to finding codes for use in direct sequence spread spectrum communications systems is described. It is based upon an analogy between codes having auto-and cross-correlation properties desirable for spread spectrum systems, and certain dynami-cal systems encountered in ergodic theory called systems with Lebesgue spectrum. Such systems are… (More)

- M R Muldoon, D S Broomhead, J P Huke
- 1998

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 = (x j) + j where is some xed map and the j are i.i.d.… (More)

- D S Broomhead, J P Huke, M R Muldoon, J Stark, J P H U K E, M R M U L D O O N
- 2004

Email alerting service here right-hand corner of the article or click Receive free email alerts when new articles cite this article-sign up in the box at the top This paper introduces a new class of models of digital communications channels. Physically, these models take account of the digital nature of the input. Mathematically , they are iterated function… (More)

- R Carretero-Gonzá Lez, J Huke, D S Broomhead, J Stark
- 1998

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the… (More)

We compare the behavior of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests… (More)

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