We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of f...

In the paper, two pre-processing methods for load forecast sampling data including multiwavelet transformation and chaotic time series are introduced. In addition, multi neural network for load forecast including BP artificial neural network, RBF neural network and wavelet neural network are introduced, too. Then, a combination load forecasting model for power load based on chaotic time series,...

An attempt is made in this study to estimate the noise level present in a chaotic time series. This is achieved by employing a linear least-squares method that is based on the correlation integral form obtained by Diks in 1999. The effectiveness of the method is demonstrated using five artificial chaotic time series, the Henon map, the Lorenz equation, the Duffing equation, the Rossler equation...

Multi –Step ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multi-step chaotic time series prediction. In the literature there is a wide range of different approaches but their success depends on the predicting performa...

Among most machine learning algorithms for optimization problem including meta-heuristic search algorithms, the solution is drawn like a moth to a flame and cannot keep away. The track of chaotic variable can travel ergodically over the whole search space. In general, the chaotic variable has special characters, i.e., ergodicity, pseudo-randomness and irregularity. To enrich the searching behav...

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and i...

in this paper, we propose a new residual analysis method using fourier series transform into fuzzy time series model for improving the forecasting performance. this hybrid model takes advantage of the high predictable power of fuzzy time series model and fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...

We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series genera...