Guo-Qun Zhong

A universal circuit for studying and generating chaos. I. Routes to chaos

In this introductory tutorial paper, we demonstrate the generality of Chuas oscillator in generating chaos and bifurcation phenomena by electronic laboratory experiments which illustrate the standard routes to chaos, and by giving a result which shows that Chuas oscillator can generate the same qualitative behavior as any member of a 21-parameter family C of continuous, odd-symmetric, piecewise-linear vector field in R/sup 3/. This result is of fundamental importance because it unifies many previously published papers on chaotic circuits and systems under one umbrella, thereby obviating the need to analyze these circuits and systems as separate and unrelated systems. Indeed, every bifurcation and chaotic phenomena exhibited by any member of the family C is also exhibited by this universal circuit. >

Implementation of Chua's circuit with a cubic nonlinearity

This paper reports an implementation of Chuas circuit with a smooth nonlinearity, described by a cubic polynomial. Some bifurcation phenomena and chaotic attractors observed experimentally from the laboratory model and simulated by computer for the model are also presented. Comparing both the observations and simulations, the results are satisfactory. >

ADAPTIVE SYNCHRONIZATION OF CHUA'S OSCILLATORS

In this letter, we study the use of adaptive controllers to maintain the synchronization of two Chuas oscillators when the channel and circuit parameters are time-varying. We present both computer simulation results and physical experimental results to verify the operation of the designs.

Experimental hyperchaos in coupled Chua's circuits

In this letter we report experimental observation of hyperchaotic attractors in open and closed chains of Chuas circuits. >

A universal circuit for studying and generating chaos. II. Strange attractors

For pt. I see ibid., vol. 40, no. 10, p. 732-44 (1993). In a companion paper, we have shown how Chuas oscillator is topologically conjugate to a class of 3D systems. In this paper, we use this result to approximate other chaotic systems in the literature which are not necessarily piecewise linear. To further illustrate the complexity of Chuas oscillator, we also include a gallery of the many attractors found in Chuas oscillator. >

Synchronization of Chua's circuits with time-varying channels and parameters

We study the use of adaptive controllers to maintain the synchronization of two Chuas circuits with time-varying channel and time-varying parameters. Both simulation results and experimental results are provided to verify the operation of the designs.

EXPERIMENTAL SYNCHRONIZATION OF CHAOS USING CONTINUOUS CONTROL

We show experimentally that two identical chaotic Chua’s circuits can be synchronized by applying the method of continuous chaos control. The presented method is especially useful for higher-dimensional systems.

Torus-doubling bifurcations in four mutually coupled Chua's circuits

Coupled oscillators are complicated high-dimensional dynamical systems. They can exhibit a wide variety of rich dynamics which could lead to novel applications in engineering. In this work we describe a torus-doubling phenomenon observed from four mutually coupled Chuas circuits. The qualitative dynamical behavior of the coupled system is robust, yet the exact behavior is very sensitive to the initial conditions and the parameter values of the Chuas circuits. We present numerical simulation results from the system model which are in good qualitative agreement with the experimental measurements.

Synthesizing arbitrary driving-point and transfer characteristics

The property of any two-terminal resistive device is characterized by its driving-point (DP) characteristic, and any two-port resistive device with zero input current and a load-independent output voltage is described by its transfer characteristic (TC). Synthesizing a two-port device with a prescribed transfer characteristic is usually easier than synthesizing a two-terminal device with a prescribed driving-point characteristic. In this paper we propose an approach to synthesize a driving-point characteristic of a two-terminal device from the transfer characteristic of a two-port device, so that the resulting DP plot of the two-terminal device is exactly the same as the TC plot of the two-port device. We also illustrate the use of digital circuitry to synthesize arbitrary transfer characteristics. This technique will benefit the design and analysis of complex nonlinear electronic circuits and systems. A variety of characteristics synthesized using this approach are presented.

Experimental evidence of locally intermingled basins of attraction in coupled Chua's circuits

Abstract We show experimentally that two coupled chaotic systems initially operating on two different simultaneously co-existing attractors can be synchronized. Synchronization is achieved as one of the systems switches its evolution to the attractor of the other one. The final attractor of the synchronized state strongly depends on the actual position of trajectories on their attractors at the moment when coupling is introduced. Coupling introduced in such systems can lead to the locally intermingled basins of attraction of coexisting attractors. Even if the initial location of trajectories on attractors A1 and A2 is known with infinite precision, we are unable to determine, on the basis of any finite calculation, in which basin this location lies and finally we cannot be sure on which attractor the evolution will synchronize. We investigate this uncertainty in chaos synchronization in numerical and experimental studies of two coupled Chuas circuits.