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Existing works on coherence resonance, i.e., the phenomenon of noise-enhanced temporal regularity, focus on excitable dynamical systems such as those described by the FitzHugh-Nagumo equations. We extend the scope of coherence resonance to an important class of dynamical systems: coupled chaotic oscillators. In particular, we show that, when a system of coupled chaotic oscillators is under the influence of noise, the degree of temporal regularity of dynamical variables characterizing the difference among the oscillators can increase and reach a maximum value at some optimal noise level. We present numerical results illustrating the phenomenon and give a physical theory to explain it.

We report experimental evidence of phase synchronization of high dimensional chaotic oscillators in a laboratory experiment. The experiment consists of a thermocapillary driven convective cell in a time dependent chaotic regime. The synchronized states emerge as a consequence of a localized temperature perturbation to the heater. The transition to phase synchronization is studied as a function of the external perturbations. The existence and stability conditions for this phenomenon are discussed.

When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable, and its basin of attraction is riddled with holes that are repelled from it. The paper discusses the role of the absorbing area for the emergence of local vs global riddling and for controlling the dynamics, once synchronization breaks down.

We report the occurrence of spontaneous synchronizing events between two semiconductor lasers, when the emission of a frequency- and intensity-chaotic driving laser is unidirectionally coupled into a second stable response laser. The driving laser is driven chaotic by delayed optical feedback, the response laser is a device-identical solitary laser. We demonstrate the onset of an episodic synchronization regime when the two lasers are spectrally detuned with respect to each other. By a joint experimental and modeling analysis we can attribute the onset and the duration of the episodes to properties of spectral overlap of both lasers. This effect can even give rise to seemingly anticorrelated intensity behavior. We expect episodic synchronization to be a generic scenario for the loss of synchronization of chaotic oscillators exhibiting frequency cycles.

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.

We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.