Experimental verification of periodic pulling in a nonlinear electronic oscillator

An experimental investigation of entrainment and the phenomenon known as periodic pulling is described. Periodic pulling refers to the incomplete entrainment of an oscillatory nonlinear system by a periodically varying driving force. The process whereby the system’s oscillation frequency is pulled toward the driving frequency stops short of complete synchronization and is interrupted at regular intervals. In this way, periodic pulling produces pulselike amplitude and frequency modulation in the system’s oscillatory response. Associated with these combined, nonsinusoidal modulations is an asymmetric, or single-sided, spectral peak made up of spectral components at frequencies incommensurate with the undriven (spontaneous) and driving frequencies. The system being investigated uses a unijunction transistor as the nonlinear element in an electrical circuit. The behavior of the system is shown to resemble that predicted for a forced van der Pol oscillator with an adjustable nonlinear restoring force. For certain ranges of driving frequency and amplitude, when the system is not entrained to the driving force, periodic pulling is shown to alter the system’s oscillatory response significantly from that expected for conventional amplitude modulation involving two sinusoids. The essential features of the periodic pulling phenomenon are observed and compared, with good agreement, to a model.