Friday, June 23, 2006


Deterministic Chaos

I am writing a knowledge sharing-attempt on this subject.Articles will be updated time to time
based on what I have studied.It is not reproduction of any book

Welcome to the world of Chaos.Happy learning !

Non-Linear Dynamic Systems

“Simple physical laws such as Newton’s law of motion on simple physical systems such as simple pendulum can turn out an irregular and seemingly random motion that is too complex to predict or compute to any given degree of accuracy in a long run”.

Some examples of chaos are : turbulence of fluid in a flow , convection ,temperature gradient etc.,

Unpredictability of weather and fluctuations of stock markets are underlined by chaos. That’s where very close relation prevails between science and economy.

For instance we had erratic reversals of magnetic poles 14 times in past 4 million years suspected to hide a erratic geo-magnetic dynamo. So, why cant be the same case for earth-quakes ?.

So chaos has its hand on ecology ,epidemiology ,economics, disturbed chemical and biological clocks , circadian rhythms of mosquito.

All physical and chemical reactions are chaotic for some initial conditions and extreme conditions ie., far from equilibrium .

Some of the examples of chaos applications are : Craniological devices such as EEG, ECG etc.,
Chaos says “A chance emerges out of necessity ”

Repeated application (or iteration) of simple recursive rule is the simpe standard tool for creating and analyzing chaos .

After a long iterative run either it can
Put (constant ) or
Repeating on itself (periodic)
Keeps changing without being repeating on itself
The last one signifies chaos.

The Chaos has sensitive dependency to initial conditions .This can be made use to create predicted or expected results.

(Note : Chaotic advectional mixing is effective than Molecular mixing ).

* chapter - 1 *
Why its called deterministic chaos ?
Non-deterministic chaos or Stochastic noise are produced as a result of unreckoned or uncontrollable forces .Eg is Brownian Movement :
Is depicted as movement of a pollen grain inside the water due to the unobserved

......Covered Later :

Logistic map
Circle map
Hamilton chaos
Strange attractor
KAM theorem

bye for now...

No comments: