Introduction - Noise-induced Phenomena in the Environmental Sciences - page 2

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Dynamical System − 0.1

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0 100 200 300 400
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(a)

Dynamical System

(b)

Figure 1.1. Schematic representation of noise-induced phenomena in (a) time and
(b) space. Nonlinear systems forced by random drivers (left-hand panels) may lead
to the emergence of ordered states in both time and space (right-hand panels).

bifurcations that would not exist in the deterministic counterpart of these systems.
Noise can also modify the stability and resilience of deterministic states and induce
coherence in the spatial and temporal variabilities of the state variables, including the
emergence of periodic oscillations or the formation of spatial patterns. The ability of
noise to induce order and organization (the so-called constructive effect of noise )is
a quite counterintuitive effect that has seldom been investigated in the environmental
science literature (e.g., May , 1972 ; Benzietal. , 1982a ; Rodriguez-Iturbe et al. , 1991 ;
Katuletal. , 2007 ). This topic concentrates on this constructive effect of noise and on
its ability to induce dynamical behaviors [i.e., states, bifurcations, spatial or temporal
coherence (or both)] that do not exist in the underlying deterministic dynamics. We
generically refer to these behaviors as noise-induced phenomena .
Figure 1.1 shows a schematic representation of some of these noise-induced behav-
iors: A nonlinear dynamical system forced by disordered random fluctuations either
in space or in time may lead to the emergence of different forms of coherence, includ-
ing for example noise-induced bistable dynamics [e.g., Fig. 1.1(a)] or morphogenesis
[e.g., Fig. 1.1(b)]. In all of these cases, noise-induced behaviors appear when the noise
intensity exceeds a critical level, whereas they disappear when it tends to zero.