Introducing Chaos Theory

Keke Gai’s PresentationRES 7023Lawrence Technological University

What is Chaos Theory?

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

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

Definition

First stated by Edward Lorentz in 1960s. Introduced by James A. Yorke and his partners a

s a new paradigm in 1975 (Yorke, 1975) Dr. Kellert (1993) defines Chaos Theory as a qual

itative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems (p.2).

Definition

Highlights the impossibility of long-term prediction for nonlinear systems.

The mathematics of chaos privileges a qualitative approach

Dynamical Models

Dynamical systems Population models Financial models

Celestial mechanics

Lorenz’s Contributions

Strange attractors The butterfly effect Origin of the Lorenz

equations Complex Behavior of

Simple Systems

Edward Lorenz

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

Difference between Random Data and Chaotic Data

Random Data Non-deterministic

Chaotic Data No asymptotically peri

odic No Lyapunov expone

nt vanishes The largest Lyapunov

exponent is strictly positive

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

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

Chaos Theory in Management

Application Example:The population fluctuations of a species

The logistic equation is:

The example is retrieved by Johnson & Burton’s (1994) article

Application Example

Plots of the logistic equation at different parameter values

Limitation

Lack analytical tractability & predictive power

Lack theoretical & empirical work in organizational adaptation, learning, and creativity

Conclusion

Chaos theory provides us with an alternative imagery

Obstacles for chaos theory research Metaphors can lead to new insights

For More Information

Please visit:

Chaostheoryresearch.wordpress.com

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/Applying-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). Tsoukas, H. (1998). Introduction: Chaos, Complexity and Organization Theory. Organization, 5(3), 291-313. Werndl, C. (2009). What are the New Implications of Chaos for Unpredictability? The British Journal for the Philosophy of Science Advance Access, 1(2

6). William J. Baumol, J. B. (1989). Chaos: Significance, Mechanism, and Economic Applications. Journal of Economic Perspectives, 3(1), 77-105.

THANK YOU FOR LISTENING

Keke Gai

Feb. 2012