Mathematical modelling of chaotic jerk circuit and its application in secure communication system

Abstract

In chaos-based secure communication schemes, a message signal is modulated to the chaotic signal at transmitter and at receiver the masking signals regenerated and subtracted from the receiver signal. In order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this chapter is to analyze the eigenvalue structures, various attractors, bifurcation diagram, Lyapunov exponent spectrum, FFT analysis, Poincare maps, while the analysis of the synchronization in the case of bidirectional coupling between two identical generated chaotic systems, has been presented. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling method scheme between two identical Jerk circuits in a secure communication system is presented in details.