Introducing
Chaos Theory
Keke Gai’s Presentation
RES 7023
Lawrence Technological University
What is Chaos Theory?
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The picture is retrieved by Shutterstock Images from http://www.shutterstock.com/pic17548057/stock-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.
Definition
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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
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Dynamical Models
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Dynamical systems
Population models
Financial models
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Celestial mechanics
Lorenz’s Contributions
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Strange attractors
The butterfly effect
Origin of the Lorenz
equations
Complex Behavior of
Simple Systems
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Edward Lorenz
The Butterfly Effect
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first described by
Lorenz in 1972
Technical name:
Sensitive
Dependence on Initial
Conditions.
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“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
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Random Data
Non-deterministic
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Chaotic Data
No asymptotically
periodic
No Lyapunov
exponent vanishes
The largest Lyapunov
exponent is strictly
positive
Where is Chaos Theory applied in?
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Career development
Geology
Mathematics
Microbiology
Biology
Computer science
Economics
Engineering
Finance
Tourism
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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
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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
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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
Reference
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Bloch, D. P. (2005). Complexity, Chaos, and Nonlinear Dynamics: a New Perspective on Career Development. Career Development Quarterly, 53(3).
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Peters, E. E. (1994). Fractal Market Analysis: Applying Chaos Theory to Investment and Economics: John Wiley & Sons, Inc.
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Werndl, C. (2009). What are the New Implications of Chaos for Unpredictability? The British Journal for the Philosophy of Science Advance Access,
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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