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Ulrich Parlitz

Publications and source records attributed to Ulrich Parlitz.

4 recordsLinked to original sources
PubMed2002

When are synchronization errors small?

We address the question of bounds on the synchronization error for the case of nearly identical nonlinear systems. It is pointed out that negative largest conditional Lyapunov exponents of the synchronization manifold are not sufficient to guarantee a small synchronization error and that one has to find bounds for the deformation of the manifold due to perturbations. We present an analytic bound for a simple subclass of systems, which includes the Lur'e systems, showing that the bound for the deformation grows as the largest singular value of the linearized system gets larger. Then, the Lorenz system is taken as an example to demonstrate that the phenomenon is not restricted to Lur'e systems.

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PubMed2001

Efficient noncausal noise reduction for deterministic time series.

We present a simple noncausal noise reduction algorithm for time series that consist of noisy measurements of the state vectors of a deterministic (chaotic) nonlinear system. The underlying dynamical system is assumed to be known and to operate in discrete time. The noise reduction algorithm is an iterative scheme for finding exact deterministic orbits close to the measured noisy orbits. Furthermore, we discuss cases where the solution is not the original orbit but homoclinic to it. (c) 2001 American Institute of Physics.

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PubMed1997

Synchronizing spatiotemporal chaos.

We show analytically and numerically that a pair of uni-directionally coupled spatially extended systems can synchronize. For the case of partial differential equations the synchronization can be achieved by applying the scalar driving signals only at finite number of space points. Our approach is very general and can be useful for practical applications since the synchronization is achieved via feeding in the response system only the information from certain (discrete) spatial locations of the drive system. We also stress some open problems in the field of synchronization of spatiotemporal chaos. (c) 1997 American Institute of Physics.

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