Chaos for communication

This work shows that chaotic signals with different power spectrum and different positive Lyapunov exponents are robust to linear superposition, meaning that the superposition preserves the Lyapunov exponents and the information content of the source signals, even after being transmitted over non-ideal physical medium. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multi-path propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non-ideal properties (dispersion and interference with periodic signals) are also discussed. These wonderful properties that chaotic signals have allow me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wavesignals, can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors.

Memristor-based Chaotic System with Upper-Lower Chaotic Attractors and Abundant Dynamical Behaviors

Memristor, a controllable nonlinear element, is able to produce the chaotic signal easily. Most of the current researchers concentrate on the nonlinear properties of memristor, whereas its ability to control and adjust chaotic systems is often neglected. Thus a memristor-based chaotic system is designed to generate double-scroll chaotic attractors in this paper. The key features of the system are as follows: (a) when the polarity of the strength of memristor is adjusted, the upper-lower double-scroll chaotic attractors will be presented in the system. Chaotic motion of the system will be weakened and suppressed by properly selecting the strength of memristor, which enables the system to generate chaotic signals or suppress chaotic interference; (b) The system has very abundant dynamical behaviors, including sustained chaos, bistability, coexisting attractors, transient chaos, transient period and intermittency. To further explain the complex dynamics of the system, several basic dynamical behaviors, such as dissipation, symmetry, the stability of the equilibria, Poincare-maps, offset boosting control, recurrence analysis, 0-1 test analysis, and instantaneous phase analysis are displayed, either analytically or numerically. Moreover, the analogy circuit of the system is constructed. Experiment results prove that the PSPICE simulation and numerical analysis are consistent, which verifies the chaotic system's capability that produces chaos. Additionally, the proposed chaotic system has a strong immunity to any Gaussian noise with the zero mean. Therefore, a convenient method is employed to detect a weak multi-frequency signal embedded in the Gaussian noise based on the proposed chaotic system and the recursive back-stepping controller. The method based on the memristor-based chaos system provides a new train of thought for detecting weak signals, which is of great significance to promote the application of memristor.