The Design and Implement of Chaotic Jerk Oscillator with Application to Secure Communication Systems Based on Chaotic Masking

Abstract

Chaotic signals have recently been of much interest as a new promising carrier frequency or an unpredictable masking signal for applications in secure wireless communication systems. Existing chaotic circuits have extensively been constructed based on threedimensional ordinary differential equations. It has recently been reported that jerk chaotic systems can generate chaotic signals through a single dynamical equation, leading to an algebraically simple mathematical model as well as a cost-effective circuit implementation. This paper presents vary simple autonomous RC chaotic jerk oscillator with nine electronic components. The chaotic jerk oscillator with nine electronic components. The nonlinearity required for chaos is implemented through the use of a well-known diode equation. Basic dynamical properties are described including equilibria, eigenvalues of Jacobian matrix, chaotic attractors, time-domain waveforms, power spectrum, and bifurcations. Potential application of such a simple autonomous RC chaotic jerk oscillator is presented in message-masking and synchronization for secure digital communications. The results show that the chaotically masked message is fully synchronized at the receiver through the use of very simple circuit. Consequently, the proposed paradigm on secure communication schemes offers not only a simple mathematical system, but also very cost-effective circuit and system implementation.