A new chaotic oscillator - Properties, analog implementation, and secure communication application

This paper reports a new 3-dimensional autonomous chaotic system with four nonlinearities. The system is studied with respect to its numerical solutions in phase space, including sensitive dependence on initial conditions, equilibrium points, bifurcation, and maximal Lyapunov exponent. It is shown that the system is dissipative and has a fractional Lyapunov dimension. Besides, a basin of attraction is determined by the Newton-Raphson's method. To show its practicality, the new system is implemented by means of an analog electronic circuit. Aperiodicity of the experimental signal is verified by means of an improved power spectral density estimator, viz., the Welch's method. Also, the correlation dimension is estimated from the experimental time series with the result confirming that the responses are deterministic chaos. Finally, an electronic design of a secure communication application is carried out, wherein a nontrivial square wave is modulated by a master chaotic signal. The modulated signal is subsequently recovered by a slave system, and the fast convergence to zero of the information recovery error substantiates the effectiveness of the design.