Abstract. In chaotic cryptosystems, it is recognized that using (very) high dimensional chaotic attractors for encrypting a given message may improve the privacy of chaotic encoding. In this paper, we study a kind of hyperchaotic systems using some classical methods. The results show that besides the high dimension, the sub-Nyquist sampling interval is also an important factor that can improve ...

BACKGROUND Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes relat...

Using the Lorenz equations, we have investigated whether unstable periodic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experimental chaotic time series. Histograms with sharp peaks occur for the Lorenz parameter value r = 60.0 but not for r = 28.0, and the sharp peaks for r = 60.0 do not correspond to any single hi...

In this paper a different algorithm is proposed to produce surrogates for pseudoperiodic time series. By imposing a few constraints on the noise components of pseudoperiodic data sets, we devise an effective method to generate surrogates. Unlike other algorithms, this method properly copes with pseudoperiodic orbits contaminated with linear colored observational noise. We will demonstrate the a...

An important financial subject that has attracted researchers' attention for many years is forecasting stock return. Many researchers have contributed in this area of chaotic forecast in their ways. Among them data mining techniques have been successfully shown to generate high forecasting accuracy of stock price movement. Nowadays, instead of a single aspects of stock market, traders need...

Local models have emerged as one of the most accurate methods of time series prediction, but their performance is sensitive to the choice of user-specified parameters such as the size of the neighborhood, the embedding dimension, and the distance metric. This paper describes a new method of optimizing these parameters to minimize the multi-step cross-validation error. Empirical results indicate...

There are many noise reduction methods for chaotic signals, but most only work over a limited signal to noise range. If chaotic signals are to be used for communications, noise reduction techniques which can handle larger amounts of noise (or deterministic noise) are needed. I describe here a method of approximating a chaotic signal by constructing possible sequences based on unstable periodic ...

A novel method for regression has been recently proposed by V. Vapnik et al. 8, 9]. The technique, called Support Vector Machine (SVM), is very well founded from the mathematical point of view and seems to provide a new insight in function approximation. We implemented the SVM and tested it on the same data base of chaotic time series that was used in 1] to compare the performances of diierent ...

Deterministic nonlinear prediction is a pow erful tec hnique for the analysis and prediction of time series generated by nonlinear dynamical systems. In this paper the use of a Kohonen netw ork asa component of one deterministic nonlinear prediction algorithm is suggested. In order to evaluate the performance of the proposed algorithm, it was applied to the prediction of time series generated b...

Time series can be transformed into graphs called horizontal visibility graphs (HVGs) in order to gain useful insights. Here, the maximum eigenvalue of the adjacency matrix associated to the HVG derived from several time series is calculated. The maximum eigenvalue methodology is able to discriminate between chaos and randomness and is suitable for short time series, hence for experimental resu...