Control of the chaotic state caused by the curent-driven ion acoustic instabilit and dynamical behavior using delayed feedback

Abstract

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.