LAUSR

The bi-stability property and transition to hyperchaos of a class of semiconductor diode-based oscillators are investigated. A simple 4D hyperchaotic oscillator proposed by Lindberg and co-workers (referred to as the LMT oscillator hereafter) is considered as a paradigm. Due to the usage of stable oscillators coupled through a non-linear resistor, this circuit has better reproducibility and higher stability and thus may be exploited for secure communication applications. In contrast to current approaches based on piecewise-linearization methods, a smooth mathematical model is derived to investigate the dynamics of the oscillator. The bifurcation analysis shows some striking transitions including period-adding, period doubling and torus breakdown routes to chaos when monitoring the control parameters in tiny ranges. More interestingly, some regions of the parameter space corresponding to the coexistence of different attractors are revealed. This phenomenon was not reported previously and thus represents an enriching contribution concerning the behaviour of such types of oscillators. The transitions to hyperchaos are contrasted with equivalent scenarios obtained from an experimental implementation of the circuit in PSpice yielding a very good agreement.