The route to chaos in a ̄uid layer heated from below is investigated by using the weak non-linear theory as well as Adomian's decomposition method to solve a system of ordinary di€erential equations which result from a truncated Galerkin representation of the governing equations. This representation yields the familiar Lorenz equations. While the weak non-linear method of solution provides sign...

Forecasting of petroleum production time series is a key task underlying scheduling of oil refinery production. In turn, forecasting requires analysing whether time series exhibits chaotic behavior. In this paper we consider chaos analysis based forecasting of time series of gasoline and diesel production. Chaos analysis is based on Lyapunov exponents and includes determination of optimal value...

An analysis of experimental data from the RFX (Reversed Field eXperiment) reversed field pinch machine [L.sion Eng. Des. 25, 315 (1995)] is carried out to investigate the possible existence of deterministic chaos in the edge plasma region. The mathematical tools used include Lyapunov exponents, Kaplan–Yorke dimension, minimum embedding dimension estimates and nonlinear forecasting. The whole an...

This paper presents an analysis/synthesis model for sound that is based on nonlinear dynamics, or chaos, theory. The inspiration is that since chaos and fractals can represent many complex naturally occurring forms, can the same be found for sound? Evidence is examined that shows how nonlinear dynamics plays a fundamental role in the generation of sounds, both musical and non-musical. Presented...

Based on the invariance principle of differential equations, a simple uniform coupling scheme is proposed to strictly synchronize almost all chaotic systems. Namely, one may synchronize highqualitatively chaotic systems by the uniform adaptive-feedback controller, i.e., a simple feedback coupling with the updated feedback strength. Unlike the usual linear feedback, the variable feedback strengt...

A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker’s, Tinckerbel’s in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos ...

The aim of this paper is to investigate the existence of Parrondo’s paradox for the logistic family fa(x) = ax(1−x), x ∈ [0, 1], when the parameter value a ranges over the interval [1, 4]. We find that a paradox of type “order + order = chaos” arises for both physically observable and topological chaos, while a “chaos + chaos = order” paradox can be only detected for the case of physically obse...

In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov’s convex regularization and via differential inclusions, the underlying discontinuous initial value problem is first recast in terms of a set-valued problem and hence it is continuously approximated by using Cellina’s Theor...

In this paper, a very recent chaos control method that stabilizes chaotic systems by introducing small perturbations in the system variables [l] and a new synchronization method that reproduces the driving signal with a single connection [2] are simultaneously applied t o small networks of chaotic electronic circuits ( the Chua circuits [3]) . \ire stabilize a Chua circuit (which acts as drive ...