Noise can stabilize a metastable state in such a way that the system remains in this state for a longer time than in the absence of noise. When this phenomenon is observed in chaos, it is called "noise-induced order." We have experimentally detected noise-induced order in the Belousov-Zhabotinsky reaction. That is, when noise is added to the chaos with the flow rate near the period-three oscillation, a decrease of the maximum Lyapunov exponent and a convergence of the Fourier spectrum are observed. Moreover, the analysis on the one-dimensional return map reveals that noise-induced order is caused by the convergence of the chaotic trajectory into the laminar region.
Controlling chaos caused by the current-driven ion acoustic instability is attempted using the delayed continuous feedback method, i.e., the time-delay auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170 (1992) 421.]. When the control is applied to the typical chaotic state, chaotic orbit changes to periodic one, maintaining the instability. The chaotic state is well controlled using the TDAS method.It is found that the control is achieved when a delay time is chosen near the unstable periodic orbit corresponding to the fundamental mode. Furthermore, when the delayed feedback is applied to a periodic nonlinear regime and arbitrary time delay is chosen, the periodic state is leaded to various motions including chaos. As a related topic, the synchronization between two instabilities of autonomous discharge tubes in a glow discharge is studied. Two tubes are settled independently and interacting each other through the coupler consisted of variable resister and capacitor. When the value of resister is changed as the strength of coupling, coupled system shows a state such as chaos synchronization.
It was found that the periodic change of the solution viscosity and density was generated in the Belousov-Zhabotinsky (BZ) reaction. This rhythmic phenomenon was observed in both the iron catalyst [[Fe(Phen)(3)](2+)-[Fe(Phen)(3)](3+)] and the cerium catalyst [Ce(III)-Ce(IV)] system, where the solution viscosity and density were synchronized with the redox potential in the in-phase mode. However, the time delay existed between the redox potential and the solution viscosity and density. The behavior of the BZ reaction was also monitored in the presence of the nonionic surfactant. This experiment revealed that, beyond the critical micelle concentration, the phase between the redox potential and the solution viscosity and density was synchronized into the antiphase mode. We suggested that the variation of the catalyst drove the oscillation of the solution viscosity and density in the BZ reaction.
We demonstrate by electronic circuit experiments the feasibility of an unstable control loop to stabilize torsion-free orbits by time-delayed feedback control. Corresponding analytical normal form calculations and numerical simulations reveal a severe dependence of the basin of attraction on the particular coupling scheme of the control force. Such theoretical predictions are confirmed by the experiments and emphasize the importance of the coupling scheme for the global control performance.
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