Autonomous piecewise damping Josephson junction jerk oscillator: microcontroller implementation, controls, and combination synchronization

Abstract

This paper evaluates the microcontroller implementation, offset boosting control, suppression of chaos, and combination of three types of synchronization in the autonomous piecewise damping Josephson junction (JJ) jerk oscillator (APDJJJO). The APDJJJO exhibits vast shapes of chaotic behaviors, bistable limit circles, bistable period-2-oscillation, and the coexistence of regular and chaotic behaviors exposed by numerical simulations. The microcontroller realization scheme of APDJJJO validates simulated dynamics. Proceeding, two constants are outlined in the rate equations of APDJJJO to achieve the linear offset boosting of constants based on the second and third state variables, respectively. The polarity of the chaotic signal of the second or third state variable can be flexibly altered by changing any of the two introduced constants while the other constant is kept at zero. When the two constants are equal, the second and third state variables can swap between bipolar and unipolar signals flexibly by altering the unique constant parameter. Moreover, theoretical probing is performed to validate the efficacy of the configured single controller engrossed in subduing chaos in APDJJJO. Lastly, the combination of three types of synchronization between two chaotic APDJJJO are analytically and numerically investigated.