Autonomous 4-D hyperchaotic oscillator and synchronization

An autonomous hyperchaotic oscillator, which is suitable for synchronization and application in secure communications, is studied. It is based on an LC oscillator and a single amplifier biquad (SAB), coupled by means of a diode. The inductor of the resonant circuit is realized in practice by using the Antoniou gyrator circuit. The oscillator is described by a set of four differential equations. Various methods for detecting chaos, such as the Lyapunov exponents, the Lyapunov dimension, the Poincareacute map, the spectrum and the phase portraits, are used, in order to confirm the chaotic behaviour of the oscillator. The synchronization of two oscillators, coupled bi-directionally, is described. Experimental results fully coincide with theoretical and simulation results.