Issues in chaos synchronization: Subharmonic destruction, multi-valued mappings, and chaotic lightwave communication

A wide range of issues concerning the theory and practice of generalized synchronization of chaos are examined in detail. Due in part to the straightforward geometrical interpretation of identical synchronization, the corresponding theory has been firmly established. However, generalized synchronization, which corresponds to the formation of a continuous mapping between non-identical sub-systems, still possesses many facets which have not been examined in depth. Thus, a comprehensive theory of generalized synchronization is still being constructed. In this dissertation, studies concerning several scarcely examined aspects of generalized synchronization are presented.; First, a mechanism is examined by which synchronization is lost in non-identical systems with different fundamental frequencies of oscillation. This mechanism, which is the subharmonic transition, is fundamentally different than previously examined mechanisms that are commonly cited in synchronization studies.; Second, an examination of the properties of the generalized synchronization mapping when it is no longer a one-to-one mapping is presented. Most previously studied characteristics of generalized synchronization concern synchronization mappings which are one-to-one and invertible. The study in this dissertation shows interesting structure when the mapping is multi-valued, and thus is not invertible.; The final portion of this dissertation concerns chaotic lightwave communication, a practical application of synchronization using erbium-doped fiber ring lasers to optically transmit a modulated bit string across a fiber optic channel using the chaotic laser intensity waveform as the carrier. Development of a successful communications scheme is a five-fold task. First, an empirical model of an erbium-doped fiber ring laser, which includes all the physically relevant variables, is derived from first principles. Next, the amount of chaos present in the laser model must be quantified. Subsequently, the computational correctness of the laser model is confirmed by direct comparison with actual output from an experimental erbium-doped fiber ring laser. After that, synchronization of two of these lasers is simulated, and the stability of the synchronization with regards to various parametric mismatches and noise is examined. Finally, the chaotic intensity waveform of the synchronized lasers is then used as a carrier to transmit and recover a digital bit string.