Chaotic Theory and Communication

Asst. Lec. Jinan N. Shehab

The most important feature of human beings is their ability to differentiate between patterns and to identify them and to estimate the differences that push them forward. These different patterns are then called mathematical symbols. Such as Newton's recognition of the pattern of planetary motion and its formulation in gravitational equations. The most important features of these equations are unambiguous and ambiguous. While we find that the most prominent feature of chaos is, and this makes us wonder how we can study then?!

Here you must stop for a moment and know what is chaos?

The word chaos has been derived from the Greeks, which refers to unpredictability. Chaos can be defined in general as the loss of coherence and order among the members of any. This group can be a human group or an industrial system. While the theory of chaos or chaos – as it is called – it is known as the latest mathematical theories of physical dealing with the subject of dynamic (dynamic) nonlinear, which exhibits a kind of random behavior known as schisms, and this random behavior either by the inability to determine the primitive conditions or The potential physical nature of quantum mechanics. Through the theory of chaos, we try to discover the hidden organization in this random phenomenon and try to establish clear rules for the study of such systems and these phenomena weather forecasts and fluids, the solar system and the market economy and the movement of financial stocks and population growth. The first to be noticed was Edward Lorenz, a meteorologist who observed by accident in 1963 that minor changes in the initial conditions of mathematical equations that mimicked the weather system during his mathematical work could lead to radically different results (For example, a sunny weather to hurricanes). It was linked to three simple mathematical equations (called the simple water polarity) and was later known as the butterfly effect to predict more accurately the weather. Lawrence was able to discover this to provide the appropriate technological conditions in his time (the beginning of the information revolution). The basis of this theory was the French mathematician Henri Poincaré, the actual theoretical founder of the theory of chaos as we know it today, when in the late nineteenth century he spoke of systems sensitive to primary conditions. Thus, we can say that the theory of chaos belongs to the dynamic systems (which change their characteristics over time) that are nonlinear and show some disorder in their behavior. This chaos is due to two main factors:

– The inability to identify primary or primitive factors with very high accuracy.

– A second factor relates to the nature of these systems themselves and their sensitivity to the very high initial conditions, which leads to radically different results in any minor change in these prerequisites. Since 1970, chaos theory has been involved in many different research fields, such as physics, mathematics, engineering, biology, chemistry, etc. There are several types of anarchic systems that differ according to the method of their generation and their equations, including: the chaotic Rossler system in chemistry. Here Lorenz's equations were optimized for chemical reactions and the Cha system, which managed to generate the laboratory jamming phenomenon using an electric circuit and Hanon. Etc.

Use chaos theory in communication

 Due to the huge development in the networks and the transfer of information, the security and safety of this information in transport or storage has become of utmost importance both on a personal level among individuals or a year in the military or medical institutions or companies … etc. Here emerged different techniques for the preservation and integrity of this information Encryption, steganography, watermark and electronic signature. In late 1989, Matthews and many researchers noticed that there was an interesting relationship between chaos, encryption and later steganography. Although there were several cryptographic methods such as DES, RSA LSB, etc., which were used for short text and data, The data is large and contains many important information, so attention is drawn to the chaotic theory of its ability to generate random numbers that appear as noise to a person whose mechanism of generation is not known and the primary values ​​and coefficients used in generating them and thus represents a fast and secure method and less expensive for encryption and steganography compared to all methods found. Where the generated numbers are used as a secret key between the sender and the user and the possibility of encrypting or hiding information stored or sent and the possibility of encrypting the transmission channel of information.