This letter demonstrates an experimental result on chaos observed in a very practical electronic circuits called the phase-locked loops. Namely, we report that chaos can in fact occur in a practical FM demodulator circuit made of a phase-locked loop IC module (MC14046B) operating under widely employed high-damping case as well as very low-damping case.

By adding a linear resistor in series with the inductor in Chua's circuit, we obtain a circuit whose state equation is topologically conjugate (i.e., equivalent) to a 21-parameter family C of continuous odd-symmetric piecewise-linear equations in R3. In particular, except for a subset of measure zero, every system or vector field belonging to the family C, can be mapped via an explicit non-singular linear transformation into this circuit, which is uniquely determined by 7 parameters. Since no circuit with less than 7 parameters has this property, this augmented circuit is called an unfolding of Chua's circuit--it is analogous to that of "unfolding a vector field" in a small neighborhood of a singular point. Our unfolding, however, is global since it applies to the entire state space R3. The significance of the unfolded Chua's Circuit is that the qualitative dynamics of every autonomous 3rd-order chaotic circuit, system, and differential equation, containing one odd-symmetric 3-segment piecewise-linear function can be mapped into this circuit, thereby making their separate analysis unnecessary. This immense power of unification reduces the investigation of the many heretofore unrelated publications on chaotic circuits and systems to the analysis of only one canonical circuit. This unified approach is illustrated by many examples selected from a zoo of more than 30 strange attractors extracted from the literature. In addition, a gallery of 18 strange attractors in full color is included to demonstrate the immensely rich and complex dynamics of this simplest among all chaotic circuits.

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol.40, no.10, October 1993), an International workshop on "Chua's Circuit: chaotic phenomena and applications" at NOLTA'93, and a book (Edited by R. N. Madan, World Scientific, 1993) on Chua's circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last 6 months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua's circuit. The robustness of this IC chip demonstrates that an array of Chua's circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua's circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua's circuit--now generally referred to as Chua's oscillator. This circuit is most significant because it is structurally the simplest (it contain only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21–parameter family of continuous odd–symmetric piecewise–linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua's Circuits, e.g., stochastic resonance, chaos–chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua's circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua's circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g., secure communication.

New communication systems via chaotic modulations are experimentally, demonstrated. They contain the wellknown chaotic circuits as its basic elements--Chua's circuits and canonial Chua's circuits. The following advantage is found in our laboratory experiments: (a) Transmitted signals have broad spectra. (b) Secure communications are possible in the sense that the better parameter matching is required in order to recover the signal. (c) The circuit structure of our communication system is most simple at this stage. (d) The communication systems are easily built at a small outlay.