The purpose of this small article is just to give a brief introduction of “Chaos Theory” and I don’t mean to go into the details in here, but if anyone is interested in learning more details and likes to do research on this field, there are some journals such as “chaos.aip.org” and “Chaos, Solitons & Fractals” from Elsevier series which can be useful for him/her.

Why the name chaos is chosen for this phenomenon? To provide a good answer let’s have a big picture of chaotic systems.

Imagine a pinball and you just release ball in it from a special location (I call it initial condition). The pins are set in a special form (Control parameters) the board has limits from two sides and the ball hitting the limits comes back into the “pinball space”!

Assume I give number to the pins on the pinball board. The ball you have dropped hits the pins and I write down the pin numbers, until the ball is out from the other side of the board. The numbers I have taken from the pins hit by the ball provide a list of numbers, I call this list “A Sequence “.  If you try releasing ball from a slightly different position (different initial condition), the ball is going to hit some other pins (may be the first pins are the same). Trying the above experiment for several times we can understand the “The Sequence” we have for each different experiment is very different. “The Sequence” is so much sensitive to the place (initial condition), you have dropped the ball and also the pins location and a very small change in them, leads to a very big difference in the Sequence.

The above simple experiment shows one the most important characteristic of a chaotic system (sensitivity to the initial conditions). After giving a small example of the chaotic systems, I would like to describe the word CHAOS: if you check the “Encyclopedia Mythica” you can see the origin of the word chaos is from the Greek word Khaos meaning “gaping void”. The reason this word is chosen for this phenomena is because of its very sensitive to the parameters and the initial conditions and it’s almost impossible to predict the system without access to all the parameters. This causes a huge amount of complexity and randomness.
During the past decades this theory attracted many researchers to it, many of the researcher where looking for a way to describe some physical systems that had complex, nonlinear and unpredictable states, such as hydraulic related systems, stock markets, seismic forces and weather forecast (Asokan et al 2005)

There are many other applications for chaos in biology, informatics, dynamics, chemistry, electronics and computer science.  One of the famous chaotic systems used is the logistic map. In 2002 Mikotajczak published a paper with the title “COMPARATIVE STUDY OF LOGISTIC MAP SERIES PREDICTION USING FEED-FORWARD, PARTIALLY RECURRENT AND GENERAL REGRESSION NETWORKS” which can be called one of the approaches to the use of chaos in predicting nonlinear systems.

In the next article I will go some more deep into the concepts of chaos and will implement a chaotic system to show how a chaotic Sequence can be useful for different applications.