Periodization of Chaotic Oscillations by Modulation of Discharge Voltage: System Response to Changes in Square-Wave Duty Cycle

Ionization waves exhibiting chaotic oscillations were periodized by modulating the discharge voltage. The oscillations were made periodic by applying modulation to the discharge voltage using a square wave. Furthermore, the dynamic behavior when the duty cycle of the square wave was varied was investigated. The behavior of the transition threshold separating the chaotic and periodic states was investigated. A difference was confirmed between the modulation value causing the transition from the chaotic state to the periodic state when the amplitude of the modulation voltage (square wave) was increased, and the modulation value causing the transition from the periodic to the chaotic state when the amplitude was decreased. The degree of periodization of the orbit was quantitatively evaluated using the largest Lyapunov exponent and the CH diagram, which confirmed the transition from the chaotic to the periodic state. Furthermore, chaotic periodization was possible with a duty cycle close to 50%.