A noise-induced signal propagation is reported in oscillatory
media with FitzHugh-Nagumo dynamics which is based on a noise-induced phase transition to excitability. This transition occurs
via a noise-induced suppression of self-excited oscillations, while the overall phase-space structure of the system is maintained. The noise-induced excitability enables the information transport in the originally oscillatory media. We demonstrate this new feature by the propagation of a wave front and the formation of a spiral in a two dimensional lattice. These spatio-temporal structures transport information and can be observed only in the presence of suitable amount of noise and not in the deterministic self-sustained oscillatory system. Thus we extend classes of nonlinear systems with signal transmission properties also to oscillatory systems, which demonstrate a noise-induced phase transition to excitability. Further on, the mechanism of noise-induced excitability provides the opportunity to control the information transport by noise via a triggering mechanism, i.e. the information channel is switched on in the presence of noise and switched off in its absence.
In the present work we review recent results concerning stochastic phenomena in semiconductor lasers with optical feedback which operate in the low-frequency fluctuation (LFF) regime. Under these conditions the output intensity of the laser shows an irregular pulsated behavior in the form of sudden intensity dropouts. In the first two sections we show numerically the existence of stochastic and coherence resonance in the dropout appearance. These resonances are caused by the help of external colored noise introduced through the pumping current of the laser. In the third section we describe a recently reported new type of stochastic resonance, where a nonlinear system shows a resonance at a frequency not present neither at its internal time scales nor at any external perturbation. This phenomenon, known as ghost resonance, is reported both numerically and experimentally.
We present here a study of multiplicative-noise Stochastic Partial
Differential Equations (SPDE) and their sensitivity to the
stochastic interpretation (Ito or Stratonovich). We analyze both static effects such as noise-induced phase transitions and dynamical ones such as the domain growth of the spatial structures in their way towards the steady state. We discuss in which circumstances a particular choice of stochastic interpretation induces qualitative changes.
We show both numerically and experimentally that a semiconductor laser prepared in an excitable state and driven by two weak periodic signals with different frequencies is able to resonate at a ghost frequency, i.e., a frequency that is not present in the forcing signal. The small signal modulation together with the complex internal dynamics of the system produces this resonance. This is an eminently nonlinear effect that agrees with the recent theoretical predictions by Chialvo et. al. [PHys. Rec. E. 65, 050902(R),2002].
We study the effect of optical injection on the dynamical behavior of a laser whose frequency drifts randomly in time. When the autocorrelation time of these random ﬂuctuations is larger than the ty ical time scales of the system dynamics,and the range of the frequency drift is larger than the injection locking range,the laser
exhibits bursting behavior at irregular times,each burst being followed by relaxation oscillations towards the unlocked state. Numerical results from a simple model agree satisfactorily with the experimentally observed behavior of an injected fiber ring laser.
We study nonlinear systems under two noisy sources to demonstrate the concept of doubly stochastic effects. In such effects noise plays a twofold role: first it induces a special feature in the system, and second it interplays with this feature leading to noise-induced order. For this effect one needs to optimize both noisy sources, hence we call these phenomena doubly stochastic effects. To show the generality of this approach we apply this concept to several basic noise-induced phenomena: stochastic resonance, noise-induced propagation and coherence resonance. Additionally, we discuss an application of this concept to noise-induced transitions and ratchets. In all these noise-induced effects ordering occurs due to the joint action of two noisy sources.
The influence of spatiotemporally correlated power-law, i.e. 1/f^\alpha$, noise on pattern formation in a two dimensional excitable medium consisting of coupled FitzHugh-Nagumo (FHN) oscillators is discussed. The signature of Spatiotemporal Stochastic Resonance (STSR) is investigated using the mutual information.
It is found that optimal noise variance for STSR is minimal, if both the spatial and temporal power spectral densities of the noise decay with a characteristic exponent of \alpha$=1. This effect is related to the band-pass frequency filtering characteristic of the FHN oscillator.
We study the effects of spatial coupling in the noise properties of microchip lasers. We demonstrate that the synchronization phenomena commonly observed in spatially coupled unstable laser applies to the quantum-noise-driven dynamics in steady-state stable laser; this allows us to predict a new method of the generation of twin laser beams. We derive simple analytical expressions for the synchronization-induced noise reduction phenomena. We observe a compete suppression of the dominant relaxation oscillations peaks in the intensity difference noise spectrum, as well as photon statistics approaching the standard quantum limit.
Encoding information in temporal chaotic signals and decoding it via chaotic synchronization between transmitter and receiver constitute nowadays a well-established technique. The method has been successfully implemented in electronic and optical systems. The latter, besides offering high speed of information transfer, provide a natural way of spatiotemporal communication through the use of broad chaotic optical wavefronts. An optical setup for spatiotemporal chaotic communications was recently proposed based on nonlinear ring cavities. In this article, we examine further in detail such a proposal, comparing two different encoding methods, namely injection and modulation. In the two cases, the correlation between input, transmitted, and output signals is estimated by means of measures taken from information theory. The influence of the message amplitude and parameter mismatch is analyzed.
Semiconductor lasers with optical feedback are prone to exhibit unstable behavior. When working near threshold with moderate to low optical feedback, intensity dropouts are observed. These intensity drops, also called low-frequency fluctuations, occur both in single-mode and multimode semiconductor lasers. In this paper, the dynamics of the power distribution between the longitudinal modes of a multimode semiconductor laser is experimentally and numerically analyzed in the low-frequency fluctuation regime. It is observed that power dropouts of the total intensity, corresponding to drops in the dominant modes of the laser, are invariably accompanied by sudden activations of several longitudinal side modes. These activations are seen not to be simultaneous to the dropouts of the main modes, but to occur after them. The phenomenon is statistically analyzed in a systematic way, and the corresponding delay is estimated, leading to the conclusion that the side mode activation is a consequence of the dropouts of the dominant modes. A multimode extension of the Lang-Kobayashi equations is used to model the experimental setup. Numerical simulations also exhibit a time delay between the side-mode activation and the power dropout of the total intensity.