Noise-induced phenomena in environmental systems - Noise-induced Phenomena in the Environmental Sciences - page 98

4
Noise-induced phenomena in environmental systems
4.1 Introduction
Environmental systems are typically forced by a number of drivers, such as climate
and natural or anthropogenic disturbances, that are not constant in time but fluctuate.
With the exception of processes dominated by deterministic oscillations (e.g., daily
and seasonal cycles), a significant part of environmental variability is random because
of the uncertainty inherent in weather patterns, climate fluctuations and episodic
disturbances such as hurricanes, landslides, earthquakes, fires, insect outbreaks, and
epidemics (e.g., Ludwig et al. , 1978 ; Benda and Dunne , 1997 ; D'Odorico et al. ,
2006b ; Gilligan and van den Bosch , 2008 ). The recurrence of random drivers in
biogeophysical processes motivates the study of how a stochastic environment may
affect and determine the dynamics of natural systems.
Over the past few decades a number of studies have contributed to the observation,
understanding, and modeling of stochastic processes in different areas of the biologi-
cal (e.g., Bharucha-Reid , 1960 ; May , 1973 ; Tuckwell , 1988 ) and earth sciences (e.g.,
Krumbein and Graybill , 1965 ; Yev j ev i c h , 1970 ; Bras and Rodriguez-Iturbe , 1994 ;
Hipel and McLeod , 1994 ), leading to the development and application of several
modeling frameworks for the study of random environmental fluctuations. This rather
rich body of literature can be divided into two major classes, depending on the role
played by noise in the dynamics of natural systems. In Chapter 3 we showed how
random environmental drivers may either cause stochastic fluctuations of the system
around the stable state(s) of the underlying deterministic dynamics ( disorganizing
effect of noise) or induce new dynamical behaviors and new ordered states ( May ,
1973 ; Horsthemke and Lefever , 1984 ) that do not exist in the deterministic coun-
terpart of the process ( organizing effect of noise). For example, noise could cause
the emergence of new stable states, determine new bifurcations, or destabilize the
stable states existing in the deterministic system. Known as noise-induced transitions
( Horsthemke and Lefever , 1984 ), these noise-induced phenomena suggest that noise
98