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

What is Chaos Theory? The picture is retrieved by Shutterstock Images from /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),

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).

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 periodic No Lyapunov exponent 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

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THANK YOU FOR LISTENING Keke Gai Feb. 2012