Dead-beat chaos synchronization and its applications to image communications

Chaos dynamics, although deterministic, are unpredictable and extremely sensitive to initial conditions. Even infinitesimal changes in the initial condition lead to an exponential divergence of orbits. In chaos dynamics, controlling chaos and synchronizing chaos have attracted increasing interest in recent years [1]. Since the pioneering work of Corroll and Pecora demonstrating an example of synchronization of chaotic systems [2], abundant research has subsequently focused on using chaotic synchronization and applying it towards communications [3]–[14]. It has been claimed that chaos-based communications offer possibly several advantages over standard spread-spectrum communications [15]–[17]. Chaotic communication systems can spread the spectrum of the information signals and simultaneously encrypt the information [18]. Moreover, chaotic systems are inexpensive due to they can be implemented by very simple circuitry. Furthermore, chaotic signals offer possibly arbitrary power levels, and the cross correlations between pieces of chaotic signals are much lower the between pieces of sinusoidal signals [15]. Therefore, based on the above-mentioned properties, chaos-based communications are potentially suitable for the field of mobile and RF communication applications [15]–[18]. In general, synchronizing analog systems is easy to be implemented. Two favorable communication schemes have been proposed [9]–[14]. In one of those schemes, chaotic masking is where the information (analog or digital) is added to one output of the chaotic system, thereby forming an information carrier. In the other scheme, chaotic modulation is where the informa-