Non-Linear Dynamics, Self-Organization and Cellular Automata Models - Environmental Modelling: Finding Simplicity in Complexity - page 48

4.2.3.1 Feedback network. Viewed in this manner, the formation of a

drainage network on a continental surface is the direct
result of positive feedback that enhances initially minor
differences in surface elevation. At the same time, how-
ever, the occurrence of negative feedback prevents the
valleys from becoming overly deep, by the deposition of
sediment in any low spots in the drainage network. Thus
a balance is maintained: while 'successful' channels (see
Section 4.4) are deepened, no channel can become too
deep too quickly. It is this nonlinear recursive interplay 7
that leads to the emergence of channel networks.

Feedback occurs when a system processes data about its
own state. Thus, to use a humanly engineered example, the
'governor' of a steam engine is an arrangement whereby a
valve is controlled by weighted arms that revolve at a rate
which is controlled by the speed of the steam engine. As
the arms rotate faster, increased centrifugal force makes
them close the valve somewhat and so slow the engine.
As the engine slows, the arms of the governor also rotate
more slowly and so open the valve a little; the engine thus
speeds up. It is the dynamic balance between the opening
of the valve ('positive feedback') and the closing of the
valve ('negative feedback') that enables the steam engine
to maintain a constant speed. This interaction between
positive and negative feedback permits the steam engine
to process data about its own state.
In general, negative feedback within a system occurs
when the system functions in such a way that the effects
of a disturbance are counteracted over time, bringing the
system back to its pre-disturbance state. In landscapes, an
example of negative feedback can occur when deposition
of coarse sediment takes place in a channel section. The
resulting increase in gradient at the downstream end of
the deposit is reflected in an increase in flow velocity
and bed shear strength, ultimately resulting in increased
erosion of the channel bed and removal of the coarse
sediment deposit, and a return to the earlier conditions.
Positive feedback takes place when a disturbance con-
tinues to force the system away from its earlier state.
Whereas negative feedback counterbalances change and
drives the system back to the pre-disturbance conditions,
positive feedback reinforces change and may lead to an
entirely new state of the system. An example of positive
feedback can occur when soil erosion exposes an under-
lying soil horizon with a low permeability, which reduces
the infiltration rate. Consequently, the rate of overland
flow production increases and, in some cases, erosion
increases as a result. 6
In self-organizing systems, feedback plays a crucial
role in the formation of spatial and temporal patterns.
An example of the role of positive feedback in landscape
evolution occurs when erosion locally lowers the surface,
resulting in an increased concentration of water and
still more erosion, until at some point a valley is formed
which

4.2.3.2 Complexity

In order to exhibit self-organization, a system must
be complex - i.e. must possess sufficient scope 8 for
component-level interactions (which can be character-
ized as positive and negative feedback) to give rise to
system-wide, emergent responses. However, while all
self-organizing systems are complex, not all complex
systems are self-organizing ( ¸ ambel, 1993: 20). At
present there is, though, no single, precise definition of
complexity (Bar-Yam, 1997; Chaitin, 1999). Gallagher
and Appenzeller (1999) loosely define a complex system
as a system with properties that cannot be described fully
in terms of the properties of its parts. Most authors do
not provide a single definition of complexity but instead
describe various characteristics of complexity.
The notion of complexity is closely tied to our con-
ceptualization of scale. Bar-Yam (1997: 258) points out
that 'The physics of Newton and the related concepts of
calculus, which have dominated scientific thinking for
three hundred years, are based upon the understanding
that at smaller and smaller scales - both in space and
in time - physical systems become simple, smooth and
without detail.' From this viewpoint, the assumption is
that even the most complex of systems, when viewed at a
'component scale', somehow 9 becomes simpler, and thus

7 Referred to as 'complicity' in Cohen and Stewart (1994); however
the term has not caught on. As Jack Cohen put it in an email to
[e-mail] on 10 December 2000: ' amore

exquisite problem for complex thinking is the problem of recur-
sion. The system doesn't simply respond to the environment, the
environment also responds to the system. The pattern of a river
bed is the result of genuine interaction of this kind, and so is
nearly every ongoing process in physics, biology or management.'
Another term for this is 'autocatalysis', see e.g. Kauffmann (1995).
8 In other words, a large number of independently varying degrees
of freedom.
9 Because of the centre-tending effect of the law of large numbers:
see e.g. Harvey (1969: 246).

...

ultimately becomes part of a larger channel

6 In some cases the exposed B horizon will have greater shear
strength and so be better able to resist detachment by the extra
flow. Here, an increase in runoff will not result in increased erosion.