摘要:

The potential to create extreme events is an inherent property of complex systems. Since our highly structured society is particularly sensitive to extreme events such as larger power failures in electric networks, stock market crashes, epedemics caused by new types of viruses, flash floods by summer storms, their potential predictability is of highest relevance. In this contribution we assume a physical point of view and concentrate on a specific phenomenon, namely on turbulent wind gusts. We show how a rather general model, namely a continuous state Markov chain, can be employed for data driven predictions of strong wind gusts. A Markov chain can represent arbitrary finite memory processes within the range of deterministic chaotic systems on the one extreme to uncorrelated white noise on the other, but its particular strenght lies in between: Nonlinear stochastic processes. Clearly, the modelling of the turbulent flow at a single site by a Markov chain is an approximation, whose accuracy will be discussed in the talk. From a statistical point of view, the focus on the prediction of extreme events implies the usage of unconventional cost junctions, such that our predictor does not neccessarily perform well on “normal” bulk events, but has a surprisingly good performance on extreme events. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846492

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular frequency, but the map is strongly non‐equivalent to the attractor. In cases where there is not phase synchronization, basic sets can still be found, but they are almost equivalent to the attractor, meaning that when there is not Phase Synchronization, the observation of the attractor by the stroboscopic map tells one few information about the final state of a typical initial condition. We base our statements in experimental and numerical results from the sinusoidally perturbed Chua’s circuit. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846493

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In this paper we present two different indices for the detection of generalized synchronization based on the fundametal idea of recurrences in phase space. We demonstrate their applicability in different model systems and analyze the influence of observational noise and non‐stationarity on these indices. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846494

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

We present a survey to a new method of analyzing experimentally gained stochastic time series. The method is based on the theory of Markov processes and does not depend on previous knowledge of model equations. An overview about the underlying technique and several applications are given. We show for the complicated case of a chaotic dynamics spoiled at the same time by dynamical and measurement noise how to extract from data the magnitude of both types of noise. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846495

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

A novel approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2laser from experimental data. We analyze this laser system in a regime of homoclinic chaos, which is able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as non‐synchronization in a broad parameter space of forcing frequency and amplitude without further experiments. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846496

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

We describe an experiment using a chaotically driven metal plate with incremental damage. Damage in the plate is manifested as a local change in the plate’s response (loss of stiffness). We develop a statistical test for Holder continuity and demonstrate its use by examining the map between responses of the undamaged plate and responses of the damaged plate at various damage levels. We show that the statistical Holder test indicates loss of differentiable synchronization between responses as the plate is damaged and can thereby serve as a detector of structural damage in similar scenarios. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846497

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Most quantitative measures of chaos (e.g., fractal dimensions or Lyapunov exponents) rely on constructing an approximation of the natural measure on a strange attractor, which requires observing the system for at least a few hundreds of cycles at fixed control parameters. Thus, it is extremely difficult to assess deterministic chaos in a real system that experiences parameter drifts on a time scale comparable to the mean dynamical period. A natural question then is: can we infer the existence of an underlying chaotic dynamics from a very short, nonstationary, time series?We present an experimental case in which this question can be answered positively. By applying topological tools to a burst of irregular behavior recorded in a triply resonant optical parametric oscillator subject to thermal effects, we have extracted a clearcut signature of deterministic chaos from an extremely short time series segment of only 9 cycles. Indeed, this segment shadows an unstable periodic orbit whose knot type can only occur in a chaotic system. Moreover, this topological approach provides us with quantitative estimates of chaos, as a lower bound on the topological entropy of the system can be determined from the knot structure. Two positive‐entropy periodic orbits are detected in a time series of about 40 cycles, suggesting that the presence of such orbits in a time series is common. Thus, nonstationarity is not necessarily an obstacle to the characterization of chaos. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1846498

出版商:AIP    

年代:1904

数据来源: AIP