A long-standing fundamental issue in nonlinear time series analysis is to determine whether a complex time series is regular, deterministically chaotic, or random. An accurate identification of the dynamics underlying a complex time series, is of crucial importance in understanding the corresponding physical process, and in turn affects the subsequent model development. A steady stream of effor...

As a research focus of intelligence algorithm, the prediction of classic noiseless chaotic time series has a great development in recent years. However, the existing prediction models cannot get good performance for real-world chaotic time series because of the interference of noise components. In order to take full advantage of the property of real-world chaotic time series, the paper proposes...

This paper introduces a novel algorithm for determining the structure of a radial basis function (RBF) network (the number of hidden units) while it is used for dynamic modeling of chaotic time series. It can be seen that the hidden units in the RBF network can form hyperplanes to partition the input space into various regions in each of which it is possible to approximate the dynamics with a b...

The selection of an embedding scheme is an important step in the modeling and prediction of chaotic dynamical systems. Theoretical work in embedding selection abounds in the literature. However in neural network research, mostly compute intensive methods for embedding selection exist. In this paper, we propose a novel embedding selection scheme based on cluster analysis. A neural network implem...

The prediction of chaotic time series with neural networks is a traditional practical problem of dynamic systems. This paper is not intended for proposing a new model or a new methodology, but to study carefully and thoroughly several aspects of a model on which there are no enough communicated experimental data, as well as to derive conclusions that would be of interest. The recurrent neural n...

The aim of this paper is to illustrate some applications of HOS within the context of chaotic time series analysis. After reviewing briefly some of the most popular methods and approaches used in chaotic signal analysis, we show how HOS may lead to some significant improvement. First, an HOS expansion of the mutual information is shown to provide an easy way to estimate the reconstruction delay...

— This study suggests a new prediction model for chaotic time series inspired by the brain emotional learning of mammals. We describe the structure and function of this model, which is referred to as BELPM (Brain Emotional Learning-Based Prediction Model). Structurally, the model mimics the connection between the regions of the limbic system, and functionally it uses weighted k nearest neighbor...

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured timeseries. The algorithm has four special features: 1. The state of the system is extracted from the time-series using delays, followed by weighted Principal Component Analysis (PCA) data reduction. 2. The prediction model consists of both a linear model and a Multi-Layer-Perceptron (MLP...

Most naturally-occurring physical phenomena are examples of nonlinear dynamic systems, the functioning of which attracts many researchers seeking to unveil their nature. The research presented in this paper is aimed at exploring eye movement dynamic features in terms of the existence of chaotic nature. Nonlinear time series analysis methods were used for this purpose. Two time series features w...

Chaotic oscillators have been designed with embedded systems like field-programmable gate arrays (FPGAs), and applied in different engineering areas. However, the majority of works do not detail issues when choosing a numerical method associated electronic implementation. In this manner, we show FPGA implementation chaotic hyper-chaotic from selection one-step or multi-step method. We highlight...