A bifurcation of transition that destroys generalized chaos synchronization is considered. This transition frequently occurs in regimes of subharmonic chaos entrainment where synchronization can be abruptly terminated due only to an almost unnoticeable change in the shape of the driving attractor. We explore the main cause of this sensitivity and ascertain the mechanism behind this transition.

The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function. Specifically, we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one-to-one, and address the issues of the existence and continuity of such mappings. The basic theoretical framework underlying the considered synchronization regimes is then developed.

The synchronization of chaotic rare-earth-doped fiber ring lasers is analyzed. The lasers are first coupled by transmitting a fraction c of the circulating electric field in the transmitter and injecting it into the optical cavity of the receiver. A coupling strategy which relies on modulation of the intensity of the light alone is also examined. Synchronization is studied as a function of the coupling strength, and we see excellent synchronization, even with very small c. We prove that in an open loop configuration (c=1) synchronization is guaranteed due to the particular structure of our equations and of the injection method we use. The generalized synchronization of these model lasers is examined when there is parameter mismatch between the transmitter and receiver lasers. The synchronization is found to be insensitive to a wide range of mismatch in laser parameters, but it is sensitive to other parameters, in particular those associated with the phase and the polarization of the circulating electric field. Communicating information between the transmitter and receiver lasers is also addressed. We investigate a scheme for modulating information onto the chaotic electric field and then demodulating and detecting the information embedded in the chaotic signal passed down the communications channel. We show full recovery with very low error for a wide range of coupling strengths.

Chaotically oscillating rare-earth-doped fiber ring lasers (DFRLs) may provide an attractive way to exploit the broad bandwidth available in an optical communications system. Recent theoretical and experimental investigations have successfully shown techniques to modulate information onto the wide-band chaotic oscillations, transmit that signal along an optical fiber, and demodulate the information at the receiver. We develop a theoretical model of a DFRL and discuss an efficient numerical simulation which includes intrinsic linear and nonlinear induced birefringence, both transverse polarizations, group velocity dispersion, and a finite gain bandwidth. We analyze first a configuration with a single loop of optical fiber containing the doped fiber amplifier, and then, as suggested by Roy and VanWiggeren, we investigate a system with two rings of optical fiber---one made of passive fiber alone. The typical round-trip time for the passive optical ring connecting the erbium-doped amplifier to itself is 200 ns, so $\ensuremath{\approx}{10}^{5}$ round-trips are required to see the slow effects of the population inversion dynamics in this laser system. Over this large number of round-trips, physical effects like GVD and the Kerr nonlinearity, which may appear small at our frequencies and laser powers via conventional estimates, may accumulate and dominate the dynamics. We demonstrate from our model that chaotic oscillations of the ring laser with parameters relevant to erbium-doped fibers arises from the nonlinear Kerr effect and not from interplay between the atomic population inversion and radiation dynamics.