Introducing Chaos Theory

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Introducing Chaos Theory

• Keke Gais Presentation
• RES 7023
• Lawrence Technological University

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What is Chaos Theory?

• The picture is retrieved by Shutterstock Images
  from http//www.shutterstock.com/pic-17548057/stoc
  k-photo-chaos-theory.html

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• The image retrieved from Ruggles, R. (1998). The
  State of the Notion Knowledge Management in
  Practice. California Management Review, 40(3),
  80-89.

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Definition

• First stated by Edward Lorentz in 1960s.
• Introduced by James A. Yorke and his partners as
  a new paradigm in 1975 (Yorke, 1975)
• Dr. Kellert (1993) defines Chaos Theory as a
  qualitative study of unstable aperiodic behavior
  in deterministic nonlinear dynamical systems
  (p.2).

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Definition

• Highlights the impossibility of long-term
  prediction for nonlinear systems.
• The mathematics of chaos privileges a qualitative
  approach

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Dynamical Models

• Dynamical systems
• Population models
• Financial models

• Celestial mechanics

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Lorenzs Contributions

• Strange attractors
• The butterfly effect
• Origin of the Lorenz equations
• Complex Behavior of Simple Systems

• Edward Lorenz

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The Butterfly Effect

• first described by Lorenz in 1972
• Technical name Sensitive Dependence on Initial
  Conditions.

• Physicists like to think that all you have to do
  is say, these are the conditions, now what
  happens next? ---- Richard P. Feynman

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Difference between Random Data and Chaotic Data

• Random Data
• Non-deterministic

• Chaotic Data
• No asymptotically periodic
• No Lyapunov exponent vanishes
• The largest Lyapunov exponent is strictly
  positive

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Where is Chaos Theory applied in?

• Career development
• Geology
• Mathematics
• Microbiology
• Biology
• Computer science
• Economics
• Engineering
• Finance
• Tourism

• Medicine
• Meteorology
• Planning
• Philosophy
• Physics
• Politics
• Population dynamics
• Psychology
• Robotics
• Hydrology

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Chaos Theory in Management

• Two traditional application of chaos theory
  (Jonathan, 1994)
• Creating a dynamical model from the structural
  equations
• Applicable when the structure equations
  describing a system that is now known

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Chaos Theory in Management

• Application Example
• The population fluctuations of a species
• The logistic equation is
• The example is retrieved by Johnson Burtons
  (1994) article

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Application Example

• Plots of the logistic equation at different
  parameter values

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Limitation

• Lack analytical tractability predictive power
• Lack theoretical empirical work in
  organizational adaptation, learning, and
  creativity

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Conclusion

• Chaos theory provides us with an alternative
  imagery
• Obstacles for chaos theory research
• Metaphors can lead to new insights

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For More Information

• Please visit
• Chaostheoryresearch.wordpress.com

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Reference

• Abraham, F. D., Gilgen, Albert R. (1995). Chaos
  Theory in Psychology. Contributions in
  Psychology, 27.
• Bloch, D. P. (2005). Complexity, Chaos, and
  Nonlinear Dynamics a New Perspective on Career
  Development. Career Development Quarterly, 53(3).
• Cartwright, T. J. (1991). Planning and Chaos
  Theory. Journal of the American Planning
  Association, 57(1).
• Davies, B. (1999). Exploring Chaos Theory and
  Experiment. Reading, Massachusetts Perseus
  Books.
• D. Hristu-Varsakelis, C. K. (2008). Evidence for
  Nonlinear Asymmetric Causality in US Inflation,
  Metal, and Stock Returns. Discrete Dynamics in
  Nature and Society, 2008(2008), 6.
• Gleick, J. (1987). Chaos Making a New Science.
  New York 10010, U.S.A. Viking Penguin Inc.
• Glendinning, P. (1994). Stability, Instability,
  and Chaos an Introduction to the Theory of
  Nonlinear Differential Equations. Cambridge CB2
  1RP, United Kingdom The University of Cambridge
  Press.
• Harney, M. (2009). Applying Chaos Theory to
  Embedded Applications. Design Article, from
  http//eetimes.com/design/embedded/4008311/Applyin
  g-Chaos-Theory-to-Embedded-Applications
• Hayek, F. A. V. (1989). The Pretence of
  Knowledge. The American Economic Review, 79(6),
  3-7.
• James A. Yorke, T.-Y. L. (1975). Period Three
  Implies Chaos. The American Mathematical Monthly,
  82(10).
• Jonathan L. Johnson, B. K. B. (1994). Chaos and
  Complexity Theory for Management. Journal of
  Management Inquiry, 3(4), 320-328.
• Kellert, S. H. (1993). In the Wake of Chaos
  Unpredictable Order in Dynamical Systems.
  Chicago The University of Chicago Press, Ltd.,
  London.
• L. Douglas Kiel, E. E. (1997). Chaos Theory in
  the Social Sciences Foundations and
  Applications The University of Michigan Press.
• Leonidas D. Lasemidis, J. C. S. (1996). Review
  Chaos Theory and Epilepsy. Neuroscientist, 2(2),
  118-126.
• Levy, David L. (2000) "Applications and
  Limitations of Complexity Theory in Organization
  Theory and Strategy", in Jack Rabin, Gerald J.
  Miller, and W. Bartley Hildreth (editors),
  Handbook of Strategic Management, Second Edition
  (New York Marcel Dekker)
• Mckercher, B. (1998). A Chaos Approach to
  Tourism. Tourism Management, 20(4), 425-434.
• Peters, E. E. (1994). Fractal Market Analysis
  Applying Chaos Theory to Investment and
  Economics John Wiley Sons, Inc.
• Ruelle, D. (1991). Chance and Chaos. Princeton,
  NJ Princeton University Press.
• Sivakumar, B. (2000). Chaos Theory in Hydrology
  Important Issues and Interpretations. Journal of
  Hydrology, 1(20).

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THANK YOU FOR LISTENING

• Keke Gai
• Feb. 2012