Differential Evolution and Deterministic Chaotic Series: A Detailed Study

This research represents a detailed insight into the modern and popular hybridization of deterministic chaotic dynamics and evolutionary computation. It is aimed at the influence of chaotic sequences on the performance of four selected Differential Evolution (DE) variants. The variants of interest were: original DE/Rand/1/ and DE/Best/1/ mutation schemes, simple parameter adaptive jDE, and the recent state of the art version SHADE. Experiments are focused on the extensive investigation of the different randomization schemes for the selection of individuals in DE algorithm driven by the nine different two-dimensional discrete deterministic chaotic systems, as the chaotic pseudorandom number generators. The performances of DE variants and their chaotic/non-chaotic versions are recorded in the one-dimensional settings of 10D and 15 test functions from the CEC 2015 benchmark, further statistically analyzed

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolut ion. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.Comment: LaTeX 2e (elsart), 17 pages, 3 EPS figures and 2 tables, accepted for publication in Physica

Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization

We describe a simple experimental implementation of the Malkus-Lorenz water wheel. We demonstrate that both chaotic and periodic behavior is found as wheel parameters are changed in agreement with predictions from the Lorenz model. We furthermore show that when the measured angular velocity of our water wheel is used as an input signal to a computer model implementing the Lorenz equations, high quality chaos synchronization of the model and the water wheel is achieved. This indicates that the Lorenz equations provide a good description of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp

A Tool to Recover Scalar Time-Delay Systems from Experimental Time Series

We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form $dy(t)/dt = h(y(t),y(t-\tau_0))$, the delay time $\tau_0$ and the functi on $h$ can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. The method turns out to be insensitive to noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators