https://popups.uliege.be/3041-539x/index.php?id=752 Index terms fr 0 https://popups.uliege.be/3041-539x/index.php?id=903 We consider two examples of extended media under the influence of additive noise: a coupled stochastic oscillators and spatial nonlinear lattice which contains overdamped oscillators. In both systems role of the additive noise is crucial. In the first system additive noise increases signal to noise ratio, resulting in stochastic resonance. In the second system additive noise causes phase transition manifesting itself in the formation of ordered spatial patterns. Surprisingly, we find parallels between two phenomena considered. Mon, 01 Jul 2024 14:06:14 +0200 Tue, 08 Oct 2024 14:13:06 +0200 https://popups.uliege.be/3041-539x/index.php?id=903 https://popups.uliege.be/3041-539x/index.php?id=749 Recent investigations showed that even weak noise acting upon a nonlinear dynamical system can have a pronounced effect on its behaviour resulting in the transitions to a new state and in qualitative change in the system's properties, e.g., the transformation of an unstable equilibrium state into a stable one, and vice versa, the occurrence of multistability, noise-induced transport (stochastic ratchets), so-called stochastic resonance, and so on. The phenomenon of noise-induced transport is closely allied to the well-known problem of fluctuational transitions from one stable state to another. The theory of such transitions and examples of the phenomena indicated are considered. Mon, 01 Jul 2024 10:17:37 +0200 Mon, 01 Jul 2024 10:17:48 +0200 https://popups.uliege.be/3041-539x/index.php?id=749