1. Introducing Chaos Theory Keke Gai’s Presentation RES 7023 Lawrence Technological University

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

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

4. 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).

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

6. Dynamical Models Dynamical systems Population models Financial models Celestial mechanics

7. Lorenz’s Contributions Strange attractors The butterfly effect Origin of the Lorenz equations Complex Behavior of Simple Systems Edward Lorenz

8. 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

9. 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

10. 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

11. 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

12. 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

13. Application Example Plots of the logistic equation at different parameter values

14. Limitation Lack analytical tractability & predictive power Lack theoretical & empirical work in organizational adaptation, learning, and creativity

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

16. For More Information Please visit: Chaostheoryresearch.wordpress.com

17. 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-Applicationshttp://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(26). William J. Baumol, J. B. (1989). Chaos: Significance, Mechanism, and Economic Applications. Journal of Economic Perspectives, 3(1), 77-105.

18. THANK YOU FOR LISTENING Keke Gai Feb. 2012