Noise-induced phenomena in zero-dimensional systems - Noise-induced Phenomena in the Environmental Sciences - page 51

3
Noise-induced phenomena
in zero-dimensional systems
3.1 Introduction
Noise is able to dramatically change the temporal dynamics of zero-dimensional
systems. Noise-induced phenomena are fascinating, often counterintuitive, and can
play an important constructive role in the behavior of several dynamical systems in
the biogeosciences. In fact, noise is not only able to generate disorder, but it may also
give rise to new ordered states and induce unexpected dynamical behaviors, which
would not be found in the deterministic counterpart of the system.
In this chapter we review some important noise-induced phenomena that were
reported in the literature, including noise-induced structural variations of the steady-
state probability density function of the state variable (noise-induced transitions),
noise-induced phenomena modifying the time correlation and power spectrum of
the temporal dynamics (stochastic resonance and stochastic coherence), and noise-
induced drift in the oscillations of the state variable.
3.2 Noise-induced transitions
The presence of noise in a stochastic dynamical system is generally associated with
disorganized random fluctuations around the stable states of the underlying deter-
ministic system. In these cases the deterministic behavior remains the skeleton of
the dynamics, while noise fades out and partly hides the characteristic features of
the deterministic system. In these conditions, as the noise intensity increases, the
system becomes more disorganized and the features of the underlying deterministic
dynamics tend to become more difficult to recognize. However, there are also systems
in which suitable noise components can give rise to new dynamical behaviors and
new ordered states that do not exist in the deterministic counterpart of the dynamics.
Known as noise-induced transitions , these behaviors are associated with structural
changes in the steady-state probability distribution of the process. These qualitative
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