Term 
Definition 
Source 

1/f noise 
S(f)=f^{—α}, where S is the signal and f is the frequency. The constant
α, is a positive real number. 
Lockwood and Lockwood (2008) 
Alternative Stable States 
A system in which the equilibrium state can be at more than one distinct
value for identical values of the control parameters. 
Lewontin (1969) 
Basin of Attraction 
The region around an attractor (equilibrium point or limit cycle) for which
all trajectories lead to the attractor. 
Holling (1973) 
Catastrophe Theory 
The analysis of degenerate critical points of potential functions to
describe discontinuous phenomena in normally continuous systems. Seven
elementary catastrophic bifurcations exist with the cusp and fold being most
commonly applied in ecology. 
Saunders (1980) 
Cellular Automata 
A discrete model consisting of a grid of cells with each cell occupying one
of a finite number of states. A set of rules parameterized by the states of the
local cells govern the change of states. 
Wolfram (1984) 
Characteristic Length Scale 
Optimum scale at which to monitor a system to establish its deterministic
dynamics. 
Johnson (2009) 
Fractal Dimension 
A rough or fragmented geometric shape that can be subdivided in parts, each
of which is, at least approximately, a reducedsize copy of the whole. 
Mandelbrot and Wallis (1969) 
Nonlinear System 
System in which either or both additivity and homogeneity fail to hold.

Scheffer et al. (2003) 
Power Law 
A polynomial relationship that exhibits scale invariance, generally of the
form, f(x)=ax^{k}. Metabolic ecology is based on the power law relationships of
allometry. 
West et al. (1997) 
SelfOrganized Criticality 
A spatial system in which a substrate can be locally redistributed to the
nearest neighbor patches to propagate further redistribution resulting in
arbitrarily large shifts in substrate. The temporal signal of selforganized
criticality is 1/f noise and the spatial pattern is fractal. 
Lockwood and Lockwood (1997) 