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.
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.