Introduction to "CHAOS"

1. WELCOME
TO MY
PRESENTATION

2. “INTRODUCTION TO CHAOS”
Presented By
Exam Roll: 1801
Reg. No: 2010-312-254
Sesssion: 2010-2011
Couse Code: 490
Department Of Mathematics
University Of Dhaka

3. Introduction
Chaos theory is a mathematical field of study which states the nonlinear
dynamical system. The phenomenon of chaos theory was introduced to the
modern world by Edward Lorenz in 1972 with conceptualization of
“Butterfly Effect”.

4.  OUTLINES
 Introduction
 History
 Definition
 Concept
 Principal
 Applications
 Controls
 Limitations
 Conclusions
 References

5. HISTORY
Chaos theory was introduced to the modern
world by Edward Norton Lorenz, a famous
American meteorologist in 1972 .
Edward Norton Lorenz (1917 – 2008)

6.  Definition :
A system, such as the weather, that develops from a set of often simple initial conditions
but behaves very differently if the initial conditions are changed even slightly.
 Example :
There are many examples of chaos in our daily life such as :
• Chaos in the traffic system.
• Chaos in the industry.
• Chaos in the classroom and so on.

7.  Concept
Chaos theory is the study of nonlinear dynamics.
• Nonlinear : change in one variable doesn’t produce the same change or
reaction in related variables.
• Dynamics : anything that moves changes or evolves in time.

8.  Principle
There are some few more principal of chaos theory. We write it as…
• Unpredictability
• Feedback
• Order or disorder

9.  The Butterfly effect
The major important point deriving from chaos is the butterfly effect.
• When a tiny variation changes the result of a system dramatically (over a
period of time), this sensitivity what we called the butterfly effect.
• The butterfly effect is the sensitive dependence on initial conditions.
• Sensitive dependence means that the development of the system depends on
a wide number of factors.
• The flap of the wings of the butterfly is a part of the initial conditions, one
set of conditions leads to a typhoon while the other set of conditions does
not.
• Butterfly Effect suggests that our present conditions can be dramatically
altered by the most insignificant change in the past.

10.  Attractor
• An attractor is a set of numerical values toward which a system tends to evolve, for
a wide variety of starting conditions of the system.
• Attractor is generated within the system itself.
• There are several types of attractors ,such as :
i. Point attractor : In this attractor there is only one outcome for the system. Death
is a point attractor for human beings.
ii. Limit cycle or periodic attractor : Instead of moving to a single state as in a point
attractor, the system settles into a cycle.
iii. Strange attractor : An attractor is called strange if it has a fractal structure. This is
the case when the dynamics on it are chaotic, but strange non-chaotic attractors
also exist.

11.  Fractals
Fractals are images of dynamic systems of the pictures of Chaos.
• A fractal is a never-ending pattern.
• They are created by repeating a simple process over and over in an ongoing
feedback loop.
• Fractal patterns are extremely familiar, since nature is full of fractals.
• For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes,
etc.

12.  Applications
 In Stock market
 In Human body
 In Traffic Jam

13. Controls
• Alter organizational parameters so that the range of fluctuations is limited.
• Change the relationship between the organization and the environment.

14. Limitations
• The major and most significant limitation of chaos theory is the feature that
defines it : sensitive dependence on initial conditions.
• The limitations of applying chaos theory are in due mostly from choosing
the input parameters.

15. Conclusions
We can find chaos theory everywhere around us, in simple pendulum, stock
market, solar system, weather forecasting, image processing, biological
systems, human body and so on. Chaotic systems are deterministic in nature
but they may appear to be random. Chaotic systems are very sensitive to the
initial conditions which mean that a slight change in the starting point can lead
to enormously different outcomes. This makes the system fairly unpredictable.
Chaos systems never repeat but they always have some order.

16. References
• [01] Sandra Patel institute of technology-A report on chaos theory
• [02] Edward N. Lorenz, the Essence of Chaos, University of Washington Press, 7-
11 (1993)
• [03] Edward N. Lorenz, ``Deterministic non-periodic flow'' in Journal of
Atmospheric Sciences, 20, 130-41 (1963)
• [04] W. Ditto and Lou Pechora, ``Mastering Chaos'' in Scientific American, 78-84
(August 1993)
• [05] S. J. Schiff, K. Jerker, D. H. Duong, T. Chang, M. L. Spans and W. L. Ditto,
“Controlling Chaos in the Brain “ in Nature, 370, 615-20 (1994)
• [06] A. Garfunkel, M. L. Span, W. L. Ditto and J. Weiss, ``Controlling Cardiac
Chaos'' in Science257, 1230-5 (1992)
• [07] Senator Al Gore, Earth in the Balance, Houghton Mifflin (1992)
• [08] Ekman and Ruble, Ergotis Theory of Chaos and Strange Attractors, The
American Physical Society, 198512.

17. THANK
YOU