What
is Chaos Theory? Description
The Chaos Theory method from Lorenz and Poincaré is a technique that can
be used for studying complex and dynamic systems to reveal patterns of order
(nonchaos) out of seemingly chaotic behaviors.
"Chaos Theory is the qualitative study of unstable aperiodic behavior
in deterministic nonlinear dynamical systems" (Kellert, 1993, p. 2). Aperiodic
behavior is observed when there is no variable, describing the state of the
system, that undergoes a regular repetition of values. Unstable aperiodic
behavior is highly complex: it never repeats and it continues to manifest
the effects of any small perturbation.
As per the current mathematical theory a chaotic system is defined as showing
"sensitivity to initial conditions". In other words, to predict the future
state of a system with certainty, you need to know the initial conditions
with infinite accuracy, since errors increase rapidly with even the slightest
inaccuracy.
This is why the weather is so difficult to forecast. The theory also has been
applied to business cycles, and dynamics of animal populations, as well as
in fluid motion, planetary orbits, electrical currents in semiconductors,
medical conditions (like epileptic seizures), and the modeling of arms races.
During the 1960s Edward Lorenz, a meteorologist at MIT, worked on a
project to simulate weather patterns on a computer. He accidentally stumbled
upon the butterfly effect after deviations in calculations off by thousandths
greatly changed the simulations. The Butterfly Effect reflects how changes
on the small scale, can influence things on the large scale. It is the classic
example of chaos, where small changes may cause large changes. A butterfly,
flapping its wings in Hong Kong, may change tornado patterns in Texas.
Chaos Theory regards organizations/businesses as complex, dynamic, nonlinear,
cocreative and farfromequilibrium systems. Their future performance cannot
be predicted by past and present events and actions. In a state of chaos,
organizations behave in ways which are simultaneously both unpredictable (chaotic)
and patterned (orderly).
Origin of Chaos Theory. History
Ilya
Prigogine, Nobel laureate, showed that complex structures could result
from simpler ones. This is like order coming from chaos. Henry Adams previously
described this with his quote "Chaos often breeds life, when order breeds
habit". Henri Poincaré was really the "Father of Chaos [Theory]," however.
The planet Neptune was discovered in 1846 and had been predicted from the
observation of deviations in Uranus' orbit. King Oscar II of Norway was willing
to give a prize to anyone who could prove or disprove that the solar system
was stable. Poincaré offered his solution, but when a friend found an error
in his calculations, the prize was taken away until he could come up with
a new solution that worked. He found that there was no solution. Not even
the laws of Sir Isaac Newton provided a solution to this huge problem. Poincaré
had been trying to find order in a system where there was none to be found.
Chaos theory was formulated during the 1960s. Significant and more practical
work was done by Edward Lorenz in the 1960s. The name chaos was coined
by Jim Yorke, an applied mathematician at the University of Maryland
(Ruelle, 1991).
Calculation of the Chaos Theory? Formula
To apply Chaos Theory, a single measured variable x(n) = x(t0 + nt) with
a starting time, t0, and a lead time, t, provides an ndimensional space,
or phase space, that represents the full multivariate state space of the system;
up to 4 dimensions may be required to represent the phase space for a chaotic
system. Thus, over a long period of time, an observed system will develop
patterns within a nonlinear time series that can be used to predict future
states (Solomatine et al, 2001).
Usage of Chaos Theory. Applications
The principles of Chaos Theory have been successfully used to describe
and explain diverse natural and artificial phenomena. Such as:
 Predicting epileptic seizures.
 Predicting financial markets.
 Modeling of manufacturing systems.
 Making weather forecasts.
 Creating Fractals. Computergenerated images applying Chaos Theory principles.
(See figures on this page.)
In a scenario where businesses operate in a turbulent, complex and
unpredictable environment, the tenets of Chaos Theory can be extremely valuable.
Application areas can include:
Steps in Chaos Theory. Process
To control chaos, the system or process of chaos has to be controlled.
To control a system, what is needed is:
 A target, objective or goal which the system should reach. For a system
with predictable behavior (deterministic) this may be a particular state
of the system.
 A system capable of reaching the target or goal.
 Some means of influencing the system behavior. These are the control
inputs (decisions, decision rules, or initial states).
Strengths of Chaos Theory. Benefits
Chaos theory has wide applicability in modern science and technology era.
Communication and management may see a paradigm shift, as will several other
business areas. Research and study in this area by academics can be extremely
useful for the business and financial world.
Limitations of Chaos Theory. Disadvantages
The limitations of applying Chaos Theory are in due mostly from choosing
the input parameters. The methods chosen to compute these parameters depend
on the dynamics underlying the data and on the kind of analysis intended,
which is in most cases highly complex and not always accurate.
Chaos theory is not as simplistic to find an immediate and direct application
in the business environment, but mapping of the business environment using
the knowledge of chaos definitely is worthwhile studying.
Assumptions of Chaos Theory. Conditions
 Small actions produce rather large consequences, creating a chaotic
atmosphere.
Book: James Geick
 ChaosMaking a new Science
Book: Ali Bulent
Cambel  Applied Chaos Theory : A Paradigm for Complexity
Book: Richard Tiplady
 World of Difference
Book: Garnett P.
Williams  Chaos Theory Tamed
Forum discussions about Chaos Theory. Below you can ask a question about this topic, share your experiences, report a new development, or explain something.

Books on Managing Chaotic Systems
I have read a lot of descriptions, definitions of chaotic (complex) systems. However I have not seen in the literature any proposition on how to manage or control or cope with (undesirable) chaotic sy...
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2 comments


Coexistence of Chaos
All things are relative to one another. "Chaos" is one of the ways to predict the events of a particle under observation....
11


Chaos Theory in Relationships
Hi I do not get along with a relative, in fact we used to live together in same house but we have not spoken now for a good few years. Recently we spoke on the phone and she said to me that the reason...
10
2 comments


Chaos Theory and the Future
Every choice you make whether it is to drink a cup of coffee or drive to the supermarket, you are creating a reality, you are creating a chain. You choose what happens to you. If you could learn how t...
10
2 comments


Ways to Deal with Chaotic Systems
We are increasingly unable to predict "infinite conditions with infinite accuracy." So we have two choices:
One, we can SIMPLIFY THE SYSTEM WE MANAGE, and try to close it off from the complexitie...
9
1 comments


Lord Buddha on Chaos...
All things appear and disappear because of the concurrence of causes and conditions. Nothing ever exists entirely alone; everything is in relation to everything else....
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Is Chaos So Chaotic?
The French mathematician Poincarre demonstrated Chaos Theory by plotting the orbit of the Earth round the Sun. He imagined a huge card at right angles to the Earth's orbit and calculated the holes pun...
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Oneness Model and Principles
What if we choose the Oneness Model instead of the Chaos Model…
These are the principles of the Oneness Model:
1. Everything is linked to others.
2. All things belong to a bigger one....
1


The Initial Conditions Used by Lorenz
I need the initial conditions used by Lorenz, and an explanation why he used those.
In Chaos Theory, we consider the equations system from Lorenz enunciate, and we don't know why he used them, bu...
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The best, toprated topics about Chaos Theory. Here you will find the most valuable ideas and practical suggestions.

Quotes on Chaos Theory
Do you know some deep, famous or funny quotes on Chaos Theory? Quotations? Proverbs? Please share them as a reaction to this posting and mention the author. To get started, here's my favorite:
'C...
47
8 comments


High Performance Teams
Based on chaos theory, Dr. Marcial Losada has developed a method to improve High Performance Teams and has established the "Losada Line" using non linear mathematics. The results are much more efectiv...
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2 comments


Forces Creating Internal and External Chaos
Note that not only the circumstances INSIDE the firm can be chaotic, but also its ENVIRONMENT, and even the RELATIONSHIPS between markets and organizations can be nonlinear.
Tetenbaum (Shifting P...
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Keep your Eye on the Big Picture
To a water molecule, whether in a glass of water or in a raging river, everything appears random and chaotic.
Thus, the only prudent way to lead, is to never, ever, lose sight of the big picture....
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Advanced insights about Chaos Theory. Here you will find professional advices by experts.

Complex Adaptive Systems Organizational Theory Definition and qualifications of complex adaptive systems capable of successfully coping with chaos:
1. A system must b...


Structure your Organization at the Edge of Chaos Organizational Development Although chaos theory was discovered decades ago, it only has emerged in recent years as a model for explaining the chao...


Complexity Principles Organizational theory Charasteristics of a conducive environemnt for complex adaptive systems:
1. Complex adaptive systems are at risk when i...



Various sources of information regarding Chaos Theory. Here you will find powerpoints, videos, news, etc. to use in your own lectures and workshops.

History of Chaos Theory Developing a Broader Perspective Towards Chaos Theory In this video an explanation of the Chaos Theory of Henri Poincarė (1903) is given.
The three body problem is expl...



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