There exist several trials to describe chaos appeared in classical or quantum dynamical systems [?]. One of the present authors introduced Information Dynamics(ID for short) [18] as a frame to discuss complexity and chaos appeared in various fields, in which he tried to find a common basis by synthesizing the state change (dynamics) and the complexity associated with dynamical systems. Since th...

We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and vice versa. We further constructed an improved mass-sprig model for the same system on the basis of data obtained from the fluid dynamical computations. A det...

The concept of molecular chaos dates back to Boltzmann [3], who derived the fundamental equation of the kinetic theory of gases under the hypothesis that the molecules of a nonequilibrium gas are in a state of “molecular disorder.” The concept of propagation of molecular chaos is due to Kac [8, 9], who called it “propagation of the Boltzmann property” and used it to derive the homogeneous Boltz...

2 Deterministic chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Dynamics of simple maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Ljapunov chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Entropies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

In time series analysis, it has been considered of key importance to determine whether a complex time series measured from the system is regular, deterministically chaotic, or random. Recently, Gottwald and Melbourne have proposed an interesting test for chaos in deterministic systems. Their analyses suggest that the test may be universally applicable to any deterministic dynamical system. In o...

Gorgonum Chaos is part of the Eridania paleolake in Terra Sirenum and displays a number prominent light-toned morphological features that bear record regional climatic conditions throughout most Martian history. Based on an intergrated analysis orbital data, we mapped 1,500 km2 area southeast Chaos. Morphologic, spectroscopic, stratigraphic analyses were used to determine age composition main g...

This Letter presents chaos synchronization of two identical Rossler and Chen systems by using active control. The proposed technique is applied to achieve chaos synchronization for the Rossler and Chen dynamical systems. We demonstrate that a coupled Rossler and Chen systems can be synchronized. Numerical simulations are used to show the effectiveness of the proposed control method.  2001 Else...

A chaotic system is one whose long term behavior is unpredictable and is sensitive to the initial conditions. This thesis explores the idea of inducing chaos in systems as a means to render them inoperable. The idea is to use resonant external perturbations to drive nonlinear oscillators into progressively higher resonant states and eventually into chaos. The advantage of this approach over con...

In this paper, the adaptive synchronization method of three coupled identical chaos systems is proposed. New generic criteria of global chaos synchronization and strict theoretical proofs are given. The unidirectional (bidirectional) coupled system will synchronize by adding three adaptive feedback gain equations. As an example, the three Rössler chaotic systems with unidirectional coupling are...