Chaos Theory
(Lorenz Poincaré)

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What is Chaos Theory? Description

Fractal (image applying Chaos Theory)The Chaos Theory from Lorenz and Poincaré is a concept that can be used for studying complex and dynamic systems to reveal patterns of order (non-chaos) 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 semi-conductors, 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, non-linear, co-creative and far-from-equilibrium 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

Another chaos theory example (fractal)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 n-dimensional 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. Computer-generated 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:

  1. 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.
  2. A system capable of reaching the target or goal.
  3. 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 - Chaos-Making 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

Special Interest Group

Chaos Theory Special Interest Group.

Special Interest Group
Special Interest Group (299 members)


Forum discussions about Chaos Theory. Below you can ask a question about this topic, share your experiences, report a new development, or explain something.

🔥 COVID-19 and its Butterfly Effect on Supply Chains and the World Economy
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a la...
Comments23 comments
topic 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...
Comments2 comments
topic 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....
topic 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...
Comments2 comments
topic 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...
Comments2 comments
topic 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 complexities of...
Comments1 comments
topic 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....
Comments1 comments
topic 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...
topic Strategies in Chaos? Consider Goldratt's Thinking Processes
The theory of constraints thinking processes of E. Goldratt are effective generic tools useful in both normal and chaotic situations. - Goldratt's current reality tree diagnoses the core conflicts a...
Comments1 comments
topic Chaos Theory and Organisational Structure
The number of structures (rules and regulations) determines the performance of organizations inversely; organizational structure is determined by by external factors. For instance, in a complex envir...
Comments7 comments
topic Why does Chaos Improve Evolutionary Algorithms?
I have presented an evolutionary algorithm using chaos theory (chaotic numbers) to solve an optimization problem. The results of the experiments show that this algorithm is much better than the same e...
Comments2 comments
topic 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. 3. All the u...
topic 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, but in...
topic Chaos is one of Physics Foibles
Chaos is one of “Physics Foibles”. Recognizing the physics foibles has led to greater understanding....

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Best Practices

The best, top-rated 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: 'Chaos...
Comments8 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...
Comments2 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 Parad...
topic 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....
Comments1 comments

topic Relevance and Implications of Chaos Theory for Strategy (Levy)
Industries are complex, dynamic and nonlinear systems, in which interdependence occurs between firms, as well as between firms and other actors in the same environment such as consumers, the governmen...
topic Using Chaos Theory to Achieve a Desired Outcome
How does one start using chaos theory to achieve a desired outcome? I can think of using an attractor for defining the result and I can use a force field diagram to describe the change I want. Howe...
Comments4 comments

Expert Tips

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...
Information Sources

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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