Search

Escape time algorithm is a classical algorithm to calculate the Julia sets, but it has the disadvantage of dull color and cannot record the iterative process of the points. In this paper, we present the equipotential point algorithm to calculate the Julia sets by recording the strike frequency of the points in the iterative process. We calculate and analyze the Julia sets in the complex plane by using this algorithm. Finally, we discuss the iteration trajectory of a single point. [ABSTRACT FROM AUTHOR]

This paper introduces a new application of the Field Programmable Analog Array. Ease of design and reprogrammability are the advantages offered by this class of analog circuits, making them an ideal environment for the implementation of chaotic circuits and their experimental characterization. Chua's circuit, a well-known paradigm of nonlinear circuits, has been used as an example of application. Experimental results show the suitability of the approach, highlighting the features of the new implementation: a fully on the fly programmable Chua's circuit has been obtained. [ABSTRACT FROM AUTHOR]

This paper treats a problem of reconstructing ordinary differential equation from a single analytic time series with observational noise. We suppose that the noise is Gaussian (white). The investigation is presented in terms of classical theory of dynamical systems and modern time series analysis. We restrict our considerations on time series obtained as a numerical analytic solution of autonomous ordinary differential equation, solved with respect to the highest derivative and with polynomial right-hand side. In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient. [ABSTRACT FROM AUTHOR]