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We have designed coupled diode resonators to study the effect of small perturbations due to weak symmetric coupling on chaotic dynamics. Our experiment clearly demonstrated that chaos of the diode resonators was suppressed so that chaotic motions were converted into periodic ones with small modifications to the attractor when an appropriate coupling signal perturbed the diode resonators. Many unstable periodic orbits were stabilized and they were very stable depending on the dynamical properties of the coupling signals. Our results suggest that coupling of signals belonging to the same class is effective in controlling chaos.

We have observed an interesting bifurcation sequence at very low driving voltages applied to a diode resonator. As the driving voltage increases, an ordinary period-doubling bifurcation appears. Further increase of the driving voltage results in a reverse period-doubling bifurcation and a sudden jump of an amplitude of the current oscillation of the diode. The experimental results were compared with the results of numerical simulations of the equivalent circuit of the diode resonator and they were in good agreement. This suggests that these low-voltage bifurcations are due to nonlinearity of the capacitance and current of the diode to the applied voltage. A simple one-dimensional map explaining these low-voltage bifurcations of the diode resonator is introduced and its properties are discussed.

The weak coupling method is demonstrated to stabilize and track the unstable orbits in the diode resonator system. Continuous tracking of the unstable orbits could be achieved over a wide range from the periodic down to the deep chaotic regime as the control parameter is varied continuously without changing the feedback control parameter. During the tracking of unstable orbits, hysteresis as well as switching of the attractors are observed and these are supposed to be the generic properties of continuous tracking.