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.

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 deterministic 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.