Chaotic Signals and their Definition

Assist. Lect. Sura Fahmy Yousif

Department of Chemical Engineering

Chaotic signals can be defined as the signals that have properties like noise signals but they are absolutely certain. This means if we have the drawn function and the initial quantities, the exact amount can be reproduced. Chaotic signals refer to the systems that have nonlinear behavior. They are distinguished from other signals or sequences that each sequence in chaotic system has private characteristics such as sensitivity to initial conditions, they have no repeated values in its sequence even if the sequence was lengthy and unpredictability and this is the most powerful characteristic in these signals. In many applications, this characteristic is exploited such as forecast of seizures and weather forecast. Recently, chaos has been used in steganography and cryptography to increase security. The direct application of these signals appears in traditional digital spread spectrum of telecommunication system. By using these signals, the information is spread over a wide range instead of using conventional periodic PN sequences. Chaotic signals are generally relying on chaos theory which is a mathematical physics that was developed in 1963 by Edward Lorenz. It is an analogously stochastic and deterministic operation that appears in a dynamical nonlinear system.

The fundamental principles of chaotic signals are: [1] Self-similarity: Over time or space, the evolution of the chaotic system gives the same appearance at various scales of observation. This property makes the chaotic system looks auto repetitive at various scales of observation. [2] Sensitivity to control parameters: Chaotic systems are very sensitive to the change of the control parameters. Different dynamics in the chaotic system can be produced depending on these parameters. The variation in the system's dynamics because of the change in the values of control parameters is called bifurcation. [3] Mixing: This characteristic means that the chaotic system is evolved in time such that any other given region is always overlapped or transformed with any given region of states. [4] Ergodicity: Similar outcomes are given for statistical measurements of the variables, no matter if these measurements are computed in time or space. The dynamical system or chaotic system when measured in time or space, gives similar statistics.