A simple two-transistor 4D chaotic oscillator and its synchronization via active control

A new simple two-transistor four-dimensional (4D) chaotic oscillator is proposed using two sub-circuits, i.e. a modified single-transistor Colpitts oscillator, and another singletransistor sub-circuit for the fourth dimension. The circuit is much simpler than two existing two-transistor 4D chaotic circuits, as it has only nine electronic components, and only eleven algebraic terms in the state equation. The latter includes only three terms of nonlinearity. The circuit offers the largest Lyapunov exponent of 0.3232, which is much higher than those of the two existing two-transistor 4D chaotic circuits. The Lyapunov dimension is also identified at 3.0807. Synchronization through active control is demonstrated as a practical example of possible applications to chaos-based secure communications.