undetectable and unpredictable.
Characteristics
There is disagreement about the formal definition of chaos, but there is
agreement that chaotic systems all possess three characteristics.
(1)
The "Butterfly Effect." X cause Y in such a way that the final state or
measure of Y is highly sensitive to the initial causal condition, Y. A small
change to X produces a disproportionately larger change in Y.
(2)
Determinism: There is no element of "chance" or "probability" in the
system. Instead, there are deterministic physical laws,
which govern the
system. Consequently, fixing a choice of initial conditions (the value or amount
of
X) will determine its entire subsequent evolution (the value or measure of
Y). There is in other words no "chance" element that
could enter after the
system has been started and alter the outcome (something reflected in the
phrase "the clockwork universe"). Another way of saying this is that it is
possible ‘in principle’ to predict uniquely the output of a given input. It is clear
from the fact that chaos is built on an exponential relationship that chaos
describes the outward appearance of what happens, not the inner reality.
Perhaps ‘organised chaos’ might be a better name for it.
(3)
Aperiodic Time and Asymptotic Behaviour. In plain language this means
that in a chaotic system there can be no regular, repetitive behaviour, no matter
how long you wait. Regularity and repetition can occur only by chance and not
by the design of the system, and the chance of these occurring is virtually
zero.
Catastrophe Theory
Introduction
Chaos theory is now treated as a part of chaos theory. It originated, however,
in the late 1960s. It received its major early formulated in a book published in
1972 by the mathematician René Thom
in his book Structural Stability and
Morphogenesis. Later, Christopher Zeeman
made some more pragmatic
development was made in the 1970s.
Continuous and Discontinuous Change
Catastrophe theory applies to non linear systems. It can be best explained by a
comparison. In the simple case, change is steady, continuous and incremental.
It happens bit by bit along a line of development. Catastrophe theory refers to
this as change over a pre-defined existing stable surface In the case of the
more complicated case,
which occurs in the domain of catastrophic theory,
change is discontinuous. It is radical and abrupt such that is entails a radical or
fundamental departure from the state of affairs before the change. However,
when the change has run its course, there is new state of stability.
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Business process engineering (BPR) can cause this type of change.
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