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Timothy D Sauer

Publications and source records attributed to Timothy D Sauer.

2 recordsLinked to original sources
PubMed2004

Reconstruction of shared nonlinear dynamics in a network.

We study a general physical network consisting of a collection of response systems with complex nonlinear dynamics, influenced by a common driver. The goal is to reconstruct dynamics, regular or chaotic, that are common to all of the response systems, working from simultaneous time series measured at the responses systems only. A fundamental theorem is stated concerning the reconstruction of the common driver. An algorithm is developed, based on the theorem, to carry out the reconstruction, and is demonstrated with several examples.

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PubMed2002

Shadowing breakdown and large errors in dynamical simulations of physical systems.

Simulations play a crucial role in the modern study of physical systems. A major open question for long dynamical simulations of physical processes is the role of discretization and truncation errors in the outcome. A general mechanism is described that can cause extremely small noise inputs to result in errors in simulation statistics that are several orders of magnitude larger. A scaling law for the size of such errors in terms of the noise level and properties of the dynamics is given. This result brings into question trajectory averages that are computed for systems with particular dynamical behaviors, in particular, systems that exhibit fluctuating Lyapunov exponents or unstable dimension variability.

Journal Article↗