1,721,171 research outputs found
Efficient noncausal noise reduction for deterministic time series
No full textWe 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
Synchronization and antisynchronization of chaotic power drop-outs and jump-ups of coupled semiconductor lasers
No full textExperimental observations and numerical simulations of synchronization and antisynchronization of low-frequency power drop-outs and jump-ups of chaotic semiconductor lasers are presented
Laser stabilization with multiple-delay feedback control
No full textStabilization of chaotic intensity fluctuations of intracavity frequency-doubled solid-state (Nd: YAG) lasers using multiple-delay feedback control (MDFC) is demonstrated by numerical simulations. It is shown that MDFC not only provides stable (cw) output for constant pump rates but also works with slowly varying pump currents, resulting in corresponding (nonchaotic) intensity modulations. (c) 2006 Optical Society of America
Hybrid systems forming strange billiards
No full textHybrid dynamical systems consist of piecewise defined continuous time evolution processes interfaced with some logical or decision making process. These switches between different evolutions are triggered if the continuous state of the system reaches thresholds in state space. In the present work we investigate hybrid systems forming a special type of dynamical systems, so-called strange billiards. They show a rich variety of dynamical behavior including some unusual bifurcations and chaos, even if the continuous part of the system evolution is just linear. By means of Poincare map techniques we discuss different dynamical behaviors. Applications to the simulation of manufacturing systems and consequences for their dynamical behavior are outlined
Modeling chaotic and spatially extended systems
No full textDifferent aspects of local modeling of chaotic time series are discussed including cross validation methods and algorithms for fast nearest neighbor search. The resulting local models are used for predicting the temporal evolution of low-dimensional and spatio-temporal systems
Prediction of spatiotemporal time series based on reconstructed local states
No full textSpatiotemporal time series are analyzed and predicted using reconstructed local states. As numerical examples the evolution of a Kuramoto-Sivashinsky equation and a coupled map lattice are predicted from previously sampled data
Robust method for experimental bifurcation analysis
No full textWe present a robust method to locate and continue period-doubling, saddle-node and symmetry-breaking bifurcations of periodically driven experimental systems. The method is illustrated from results obtained for an electronic implementation of a Duffing oscillator
Modeling parameter dependence from time series
No full textTwo approaches for modeling of parameter dependence of dynamical systems from time series are investigated and applied to different examples. For both methods it is assumed that a few Lime series are available that have been measured for different (known) parameter values of the underlying (experimental) dynamical System. The objective is to model the changing dynamics of the system as a function of its parameters and to use this for experimental bifurcation analysis. Using parametrized families the tasks of modeling the dynamics and of modeling its parameter dependence are separated. Technical difficulties that may occur with this approach are discussed and illustrated. An alternative are extended state space models where both modeling, tasks are treated simultaneously. To obtain reliable models from a few time series only, ensembles of models are employed that show very good extrapolation and generalization properties
Synchronization and control of coupled Ginzburg-Landau equations using local coupling
No full textIn this paper we discuss the properties of a recently introduced coupling scheme for spatially extended systems based on local spatially averaged coupling signals [see Z. Tasev et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. (to he published); and L. Junge er al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2265 (1999)]. Using the Ginzburg-Landau model, we performed an extensive numerical examination of this coupling scheme, i.e., a complete scan through the relevant coupling parameters. Furthermore, we demonstrate suppression and control of spatiotemporal chaos, e.g., stabilizing the homogeneous steady state and spatially localized control. As an application all model parameters of the Ginzburg-Landau equation rue estimated given only the local information of the system
Stabilizing unstable steady states using multiple delay feedback control
No full textFeedback control with different and independent delay times is introduced and shown to be an efficient method for stabilizing fixed points (equilibria) of dynamical systems. In comparison to other delay based chaos control methods multiple delay feedback control is superior for controlling steady states and works also for relatively large delay times (sometimes unavoidable in experiments due to system dead times). To demonstrate this approach for stabilizing unstable fixed points we present numerical simulations of Chua's circuit and a successful experimental application for stabilizing a chaotic frequency doubled Nd-doped yttrium aluminum garnet laser
- …
