物件導向軟體之架構(Object-Oriented Software Construction)探討

The synchronization of chaotic systems

Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical importance from such measurements. They discuss methods for (1) separating the signal of physical interest from contamination ("noise reduction"), (2) constructing an appropriate state space or phase space for the data in which the full structure of the strange attractor associated with the chaotic observations is unfolded, (3) evaluating invariant properties of the dynamics such as dimensions, Lyapunov exponents, and topological characteristics, and (4) model making, local and global, for prediction and other goals. They briefly touch on the effects of linearly filtering data before analyzing it as a chaotic time series. Controlling chaotic physical systems and using them to synchronize and possibly communicate between source and receiver is considered. Finally, chaos in space-time systems, that is, the dynamics of fields, is briefly considered. While much is now known about the analysis of observed temporal chaos, spatio-temporal chaotic systems pose new challenges. The emphasis throughout the review is on the tools one now has for the realistic study of measured data in laboratory and field settings. It is the goal of this review to bring these tools into general use among physicists who study classical and semiclassical systems. Much of the progress in studying chaotic systems has rested on computational tools with some underlying rigorous mathematics. Heuristic and intuitive analysis tools guided by this mathematics and realizable on existing computers constitute the core of this review.

The analysis of observed chaotic data in physical systems

Hawaii International Conference on System Sciences

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Art of electronics

The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors Rk. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual chaotic signals, v(t)=(v1+v2)/2. The corresponding differential equations have been derived. The results of both, numerical simulations and hardware experiments are presented. The coupling coefficient k∝1/Rk should be small to avoid mutual synchronisation of the individual oscillators. The spectrum of the Lyapunov exponents (LE) have been calculated versus the coefficient k. For weakly coupled oscillators there are two positive LE indicating hyperchaotic behaviour of the overall system.

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Hyperchaos in coupled Colpitts oscillators

An extremely simple 4-D chaotic oscillator is presented. It contains a single opamp, two LC circuits and a diode used as a nonlinear device. The chaotic oscillations have been characterised using the correlation dimension of the strange attractor, the Lyapunov exponents and the Lyapunov dimension. The dimensions are found to be >3.

Simple 4D chaotic oscillator

A fourth-order hyperchaotic oscillator is described. It contains a negative impedance converter, two gyrators, two capacitors and a diode. The dynamics of the oscillator is shown to be characterised by two positive Lyapunov exponents. The performance of the circuit is investigated by means of numerical integration of appropriate differential equations, hardware experiments and PSPICE simulations.

Hyperchaotic oscillator with gyrators

On-off intermittency in spin-wave instabilities

A novel version of the chaotic Colpitts oscillator is proposed. It contains two bipolar junction transistors coupled in series. The resonance loop consists of an inductor and three capacitors. The two-stage oscillator, compared with the classical circuit, enables the fundamental frequency of chaotic oscillations to be increased by a factor of three. The PSpice simulations performed with 9 GHz threshold frequency transistors demonstrate that the highest fundamental frequencies of chaotic behaviour are 1 and 3 GHz for the classical and the two-stage Colpitts oscillator, respectively.

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Antanas Čenys

Papers

Hyperchaos in coupled Colpitts oscillators

Simple 4D chaotic oscillator

Hyperchaotic oscillator with gyrators

On-off intermittency in spin-wave instabilities

Two-stage chaotic Colpitts oscillator