Parametric entrainment control of chaotic systems

Regulating noise-induced spiking using feedback

We report successful manipulation of the noise provoked spiking behavior using delayed feedback control. Experiments were performed in a three electrode electrochemical cell under potentiostatic conditions. The uncontrolled system exhibited noise invoked oscillations whose regularity was quantified using normalized variance (NV). Superimposing delayed feedback, for appropriate values of delay (t), an enhancement in the regularity of the spike sequence was attained. Numerical simulations corroborated experimental observations.

Delay-induced resonances in an optical system with feedback

We study the influence of the delay time in the response of a delayed feedback system to external periodic driving. The nonlinear system we consider is a semiconductor laser with optical feedback operating in the low-frequency fluctuation regime. We numerically examine the consequences of varying the external cavity length of the system when a weak modulation is introduced through the laser's pump current. The harmonic modulation is seen to lead to a partial periodic entrainment of power dropouts, and the distribution of time intervals between the dropouts exhibits resonances with certain delay times. In other words, the response of the system to the external modulation is enhanced for particular values of the external cavity length. The same effect can be observed in the presence of noise, indicating that stochastic resonance can be enhanced or degraded depending on the feedback time.

Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design

The synchronization of two chaotic systems with uncertainties is studied in this paper. A feedback controller is provided based on a sliding mode control design. A kind of extended state observer is used to compensate for the systems' uncertainties, such as the structure difference or parameter mismatching, using only the available synchronizing error. Then the feedback controller becomes physically realizable based on the states of the observer, and can be used to synchronize two continuous chaotic systems. Illustrative examples of the synchronization of Duffing and Van der Pol oscillators as well as two Lorenz systems with parameter mismatching are proposed to show the effectiveness of this method.

Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis

We stabilize unstable periodic orbits of a fast diode resonator driven at 10.1 MHz (corresponding to a drive period under 100 ns) using extended time-delay autosynchronization. Stabilization is achieved by feedback of an error signal that is proportional to the difference between the value of a state variable and an infinite series of values of the state variable delayed in time by integral multiples of the period of the orbit. The technique is easy to implement electronically and it has an all-optical counterpart that may be useful for stabilizing the dynamics of fast chaotic lasers. We show that increasing the weights given to temporally distant states enlarges the domain of control and reduces the sensitivity of the domain of control on the propagation delays in the feedback loop. We determine the average time to obtain control as a function of the feedback gain and identify the mechanisms that destabilize the system at the boundaries of the domain of control. A theoretical stability analysis of a model of the diode resonator in the presence of time-delay feedback is in good agreement with the experimental results for the size and shape of the domain of control. (c) 1997 American Institute of Physics.