Continuous control of ionization wave chaos by spatially derived feedback signals

Abstract

In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback technique. The control strategy is derived from the time-delayed autosynchronization method. Two spatially displaced points of observation are used to obtain the control information, using the propagation characteristics of the chaotic wave.

Lyapunov stability of charge transport in miniband semiconductor superlattices

“…2,3 For example, the knowledge of several largest Lyapunov exponents can be used for chaos control through "unstable periodic orbit stabilization" 3,4,62,63 or for characterization of different types of chaos synchronization [64][65][66] in plasma or electronic devices.…”

Delayed feedback control of chaos

“…Bielawski et al (1994), Basso et al (1997a,b) and Lu et al (1998) applied the DFC to laser systems. Pierre et al (1996) investigated the DFC to a gas discharge system, Mausbach et al (1997) stabilized ionization wave chaos, Fukuyama et al (2002) controlled chaos caused by the current-driven ion acoustic instability and Gravier et al (2000) stabilized drift waves in a magnetized laboratory plasma. An application of the DFC to a hydrodynamic system, namely, a chaotic Taylor-Couette flow, was considered by Lüthje et al (2001).…”

“…The wave character of dynamics in some systems allows a simplification of the DFC algorithm by replacing the delay line with the spatially-distributed detectors. Mausbach et al (1997) reported such a simplification for an ionization wave experiment in a conventional cold cathode-glow discharge tube. Owing to dispersion relations, the delay in time is equivalent to the spatial displacement and the control signal can be constructed without using the delay line.…”

Numerical investigations on strong pattern selecting Eckhaus instabilities in neon glow discharges

“…In recent experiments the nonlinear properties of ionization waves including ionization turbulence were investigated. [2][3][4][5][6][7] There were reports on period doubling, torus deformation, chaotic behavior, transition to turbulence, and noise induced pattern formation. 8 Frequently, the transition from the homogeneous state to a traveling wave pattern is performed by a supercritical Hopf bifurcation.…”