Synchronization and desynchronization under the influence of quasiperiodic forcing

Basin bifurcations in quasiperiodically forced coupled systems

We study the effect of quasiperiodic forcing on a system of coupled identical logistic maps. Upon a variation of system parameters, a variety of different dynamical regimes can be observed, including phenomena such as bistability and multistability. At the bifurcation to bistability, in a manner reminiscent of attractor expansion at interior crises, there is an abrupt change in the size of attractor basins. In the bistable region, attractor basins undergo additional bifurcations wherein holes and islands are created within the basins when system parameters change. These can be understood by examining critical surfaces for the coupled system.

Dynamic control by sinusoidal perturbation and by Gaussian noise of a system of two nonlinear oscillators: computation and experimental results

In this paper we report numerical and experimental studies of the dynamic control of the inter-anode plasma of a double electrical discharge and of a system of two coupled nonlinear oscillators modeling this plasma. We compare the transition between chaotic dynamics and periodic dynamics induced by a sinusoidal perturbation and by small-dispersion Gaussian noise. Besides considerable differences between the effect of the two types of perturbation we also find important similarities. For small amplitude, both the sinusoidal and the white noise perturbations can induce the system to change from chaotic to regular dynamics. In the case of sinusoidal perturbation, the transition time from the chaotic to regular state has a definite duration that depends on the values of the perturbation parameters. The suppression of the perturbation has no influence on the state - the system remains in the same regular state. Subsequent reinstatement of the same type of perturbation with the same amplitude does not change the periodic state of the system but, for considerably higher amplitude, the system is switched back to its chaotic state. For moderate-amplitude sinusoidal perturbation, intermittent transitions between the chaotic and regular states is observed. Most of these predictions of the model have been observed experimentally in a system of two coupled electrical discharges. Our results suggest practical methods that can be used for controlling the discharge plasma dynamics.