What is the Catastrophe Theory? Description
Catastrophe Theory (CT) (René Thom) is a mathematical treatment of continuous
action producing a discontinuous result. This theory is related to Chaos Theory.
Although it was developed quite separately, it is now seen as a part of Chaos
Theory.
Although of a highly mathematical nature, the essence of CT is: to understand
change and discontinuity in systems. If a System is ‘at rest’ (ie not undergoing
change), then it will tend to occupy a preferred stable state, or at least
a defined range of states (Outcome Basin). If a System is subjected
to change forces, then
the System will initially try to react in such a way that it absorbs the stresses.
Furthermore, if it is given the chance, the system will attempt to regain
its preferred stable state. If, however, the change forces are so strong that
they can't be absorbed, then a Catastrophic Change may occur and a
new preferred stable state or range of states is established. There is no
continuous way back to the 'old' stable state.
An analogy demonstrates the principle. Imagine that a bottle is placed on
a desk. It is in a stable state, not changing, what is called Stable Equilibrium.
Now imagine pushing the neck of the bottle away from you slowly with your
finger, not too far. It is now undergoing change but the bottle is absorbing
the change in a continuous manner. It is in Unstable Equilibrium; if you release
your pressure, the bottle will revert towards its stable and preferred position.
However if you continue to push the neck of the bottle, at some point it will
fall. It is now in a new stable equilibrium state. A Catastrophic Change has
occurred. A discontinuous change has happened: once the bottle started to
fall over, there was no intermediate stable state available until the bottle
had hit the desk.
Thom’s ideas mean that Systems may change through a combination of continuous
and discontinuous change patterns. This is related to Chaos Theory because
the bottle is either standing up or is lying down. These positions describe
the possible Outcome Basins (see Chaos Theory). There are positions which
it will never be in, because they are positions of intrinsic instability.
There are seven elementary catastrophes: fold, cusp, swallowtail,
butterfly, hyperbolic umbilic, elliptic umbilic, and parabolic umbilic.
Subspecializations of Catastrophe Theory include: Bifurcation Theory,
Nonequilibrium Thermodynamics, Singularity Theory, Synergetics, and Topological
Dynamics.
Origin of the Catastrophe Theory. History
Now regarded as part of Chaos
Theory, Catastrophe Theory was developed in the late 1960s and presented
quite independently in 1972 by the mathematician René Thom in his book:
"Structural Stability and Morphogenesis". Thom hoped to be able to predict
the behavior of complex 'chaotic' systems. It was further developed on a more
pragmatic level by E.C. Zeeman in the 70s.
Usage of the Catastrophe Theory. Applications
The method can be used to understand and to predict the behavior of complex
systems. Such as:
 Stock exchanges.
 Locust infestations.
 Biological change.
 Behavior of bridges.
 Attempts to apply Thom's theories to organizations so far had
little real success, due to the large number of variables involved.
Steps in the Catastrophe Theory. Process
CT has many implications for the discipline of
Change Management and Organizational
Development.
There is a form of change which is smooth, continuous and incremental. This
is the general form of change under Business Process Improvement initiatives
(BPI) such as Kaizen,
Total Quality Management
(TQM) and Six Sigma. In CT terms, this
is change over a predefined existing stable surface.
There is another form of change which is ‘catastrophic’, abrupt, radical,
a fundamental departure from what went on before the change. This type of
change is quite often the consequence, for example, of
Business Process Reengineering (BPR). This
type of change is not ‘continuous’  in CT terms there is a catastrophic change
to a new definition of stability.
‘Real’ change is therefore more like BPR. Else there is simply improvement.
Which of course may be all that's needed to solve the specific problem! The
challenge for change specialists is in deciding when radical change is needed
versus an incremental improvement. But the choice is not straightforward since
radical change will inevitably result in a period of 'Chaos', while the ‘new’
stability is found and defined. This ties up with the recognized 'unfreezing/freezing'
methods of Change Management.
And then of course radical change may be forced upon the organization at times.
And there may be no smooth (continuous) way of taking the organization from
where it is, towards where it must be, so it is futile to assume that such
a path is available.
Strengths of the Catastrophe Theory. Benefits
 The ideas help to understand the real experience of Change Management
and the ideas in Chaos Theory. CT shows why real Change is a hazardous business.
 It does away with the thought that organizations can be varied along
'spectrums' of variable values. There are probably only a few really stable
combinations available.
 The theory shows why change cannot be 'managed' as such, but may be
influenced.
 The theory deals with the idea of 'form' (Gestalt)
and change of form. A novel way perhaps to view organizations.
Limitations of the Catastrophe Theory. Disadvantages
 The significance of Thom's work to understand organizational behavior
is more qualitative than quantitative at the moment.
 Predicting the behavior of even the simplest complex systems
still remains a difficult challenge.
 Thom failed in his aspiration to describe complex systems where there
are many (more than 5) significant variables. Predicting the behavior of
very complex systems (organizations) is likely to remain impossible forever.
Book: Alas all reading
materials that go beyond what's written here, quickly become deep in Mathematics!

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Chaos Theory 
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