A Weak Signal Detection Application Based on Hyperchaotic Lorenz System

Abstract

Due to accurate capability to detect weak signal, chaotic oscillators have become an interesting topic for many scientific researches. In this paper, two hyperchaotic Lorenz systems are presented to detect weak signal. These systems are chosen because of their parametric variety and high applicability. Dynamic behaviors of two hyperchaotic systems are analysed in detail. For this purpose, the Lyapunov exponent values and bifurcation behaviours of two hyperchaotic systems are analysed for weak signal detection applications. The relationship between the system state and the amplitude of the weak signal is defined by examining the Lyapunov exponents of the system. So, dynamic characteristics of two chaotic oscillators are observed by this way. The critical chaotic parametric threshold value of a chaotic system is easily determined by the bifurcation analysis. The bifurcation threshold value named as tangent bifurcation point is the most suitable one to detect weak signal. For this purpose, the tangent bifurcation points of these systems are determined via bifurcation analysis. Additionally, weak signal detection applications of two hyperchaotic systems are also studied. The applicability of the proposed systems is shown by these applications. These systems also detect the weak signal with low signal to noise ratio (SNR). Simulation results obtained from Matlab-Simulink® program verify the studied method.

Keywords

• bifurcation
• chaotic systems
• hyperchaos
• Lyapunov method
• signal to noise ratio
• weak signal detection