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In this paper a systematic approach, based on the linear-state-observer design for constructing two chaotically synchronized systems, is developed. The proposed method is then applied to suggest a means to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Furthermore, two well-known chaotic systems, Rossler and Lorenz, and a hyperchaotic ROssler system are considered as illustrative examples to demonstrate the effectiveness of the proposed approach. Index Terms - Chaos, chaotic synchronization, secure communication, state observer.

Torque per unit velocity is a practical method to study the subsynchronous resonance instability of electric power systems. The torque per unit velocity method is justified as an eigenvalue perturbation technique and extended to power systems with thyristor switching devices and multiple torsional modes. A new method to estimate the damping of the swing mode is proposed.

In a chaotic switching scheme, a binary message signal is scrambled by two chaotic attractors. In this paper we present examples to show how generalized chaotic synchronization (GS) can be used to break chaotic switching schemes. Since GS is a very robust phenomenon, we find that an intruder can recover the binary information signal from chaotic switching schemes without knowing both the structure and parameters of the chaotic transmitter. The breaking method presented in this paper is not sensitive to the order of the transmitter, which means that even in a chaotic switching scheme which uses two hyperchaotic systems, the degree of security may still be low. The simulation results for both low order and high order transmitters are presented.

A new alternative is described for the clock-distribution problem. The main feature of the new scheme is that a number of stations arbitrarily located on a single reference line independently derive a clock that is aligned to a common systemwide phase. The central principle is that the midtime between appearances of an isolated pulse traveling down and back on a reference line is the same, regardless of the point of observation. This principle is adapted for clock distribution by the periodic injection of a reference pulse onto a single conductor, reflection of this pulse at the end of the reference line, and generation of a local clock at all stations (such clock being phase-locked to the interval midtime by a special PLL circuit). The paper describes the method and gives a theoretical performance analysis and measured results from an experimental system. The experiments achieve a subnanosecond skew over 30 m on a coaxial cable that has an uncompensated delay of 147 ns. This method should be considered for applications from the millimeter scale on chip to the kilometer scale in radio astronomy antenna arrays. Possible advantages include reduced wiring, reduced tuning, reduced EMI, and/or power consumption and easier in-service growth, relative to conventional methods for the same performance objectives.

By combining the technique of observer design in nonlinear control systems theory and the technique of phase space reconstruction in nonlinear dynamical systems theory, we show that synchronization of smooth (hyper)chaotic systems can be attained with any scalar transmitted signal. The proposed method has been illustrated via two examples. Index Terms - Chaos, hyperchaos, synchronization theory.

Because the conventional chaos masking communication scheme is vulnerable to dynamics-based and identification-based attacks, in this paper, we develop a robust digital secure communication scheme by exploiting sporadic coupling synchronization of Lorenz system. The new scheme can not only withstand the attacks effectively but also improves the frequency efficiency and noise resistibility, etc. The secure property and system performance are theoretically analyzed. Computer simulations are performed to illustrate the effectiveness and efficiency of our new scheme. Index Terms--Chaos, digital communication, synchronization, security.

Optimal synchronization of two identical chaotic systems coupled in a drive/response manner is considered in the paper. We derive a relationship between the mean square synchronization error and the coupling parameters in the presence of noise. By minimizing the mean square synchronization error with respect to the coupling parameters, an optimal synchronization, which minimizes the synchronization error between the drive and response systems, can be achieved. It is shown that the optimal coupling parameters depend on both the global and local Lyapunov exponents of the chaotic drive system. However, they are independent of the noise power. We apply this approach to design optimal synchronization for various chaotic systems. The optimal design is then applied to chaotic communication and it can recover the information signal efficiently. Simulations show that our theoretical results are in good agreement with the numerical analysis. Index Terms--Chaos, optimal design, synchronization.

In a digital communications system, data are transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based coherent receivers have advantages over noncoherent receivers in terms of noise performance, bandwidth efficiency (in narrow-band systems) and/or data rate (in chaotic systems). These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. In Part I, the theory and operation of conventional communications systems were surveyed and possible fields of application of chaotic communications were identified. In Part II, the theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described. In Part III, examples will be given of chaotic communications schemes with and without synchronization, and the performance of these schemes is evaluated in the context of noisy, bandlimited channels. Index Terms - Chaos, communication systems, digital communication, digital modulation, spread spectrum communication.