TRANSIENT CHARACTERISTICS BETWEEN PERIODIC ATTRACTORS STABILIZED BY CHAOS CONTROL IN A SEMICONDUCTOR LASER

We investigate the transient response time between periodic attractors stabilized by chaos control methods in a semiconductor laser. We use the revised occasional proportional feedback (ROPF) method to shorten the transient response time and compare it with the high frequency injection (HFI) method. A chaotic attractor is stabilized resulting in two different periodic attractors (period-1 and period-6) under different control parameters, and the transient response time is measured as one of the stabilized periodic attractors is switched to the other. During the transition, the trajectory approaches a certain unstable periodic orbit (UPO), and the distance between the trajectory in the phase space and the UPO can be described as an exponential function of the transient response time. Since the trajectory can directly converge into the periodic orbit by using the ROPF method, the transient response time obtained by the ROPF method can be shortened more than that obtained by the HFI method.

CONTROLLING CHAOS IN A TWO-WELL OSCILLATOR

The chaotic dynamics of a nonlinear buckled elastic beam are shown to be controllable in a periodic orbit using a digital occasional proportional feedback control circuit. The method is similar to that developed by Hunt [1991] and does not require a detailed knowledge of the underlying two-dimensional map. The control is effected by perturbing the potential wells synchronously with the forcing function. Experiments show that the system possesses both periodic orbits and strange attractors different than those of the uncontrolled system.

Controlling chaos in electronic circuits

Chaotic oscillations in electronic circuits are rather an unwanted phenomenon. We describe various control concepts the goal of which is to suppress chaos and to achieve a desired type of dynamic behaviour such as stable fixed point or a periodic orbit. The control concepts described here include: (i) system parameter variation; (ii) chaotic oscillation absorber; (iii) entrainment; (iv) linear feedback control; (v) time-delayed feedback, (vi) methods for stabilizing unstable periodic orbits: occasional proportional feedback and sampled input waveform methods. Advantages and drawbacks of these methods are described. Control towards chaotic states having several potential applications is also considered.

CONTROLLING CHAOS IN A SIMPLE AUTONOMOUS SYSTEM: CHUA’S CIRCUIT

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua’s circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua’s circuit’s double-scroll attractor, applying corrections in each of these regions during a single orbit.

CONTROLLING CHAOS IN CHUA'S CIRCUIT

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua's circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua's circuit's double-scroll attractor, applying corrections in each of these regions during a single orbit.