Autonomous snap oscillator with only one steady state: dynamical probing, controls, pseudo-random number generation and difference synchronization

Abstract

The theoretical probing, microcontroller implementation, amplitude controls, chaos control, -pseudo-random number generation (PRNG), and difference synchronization of autonomous snap oscillator with only one steady state (ASOOSS) are studied in this paper. The ASOOSS exhibits self-excited complex attractors, periodic oscillations, coexistence of chaotic hidden attractors with a stable steady state, and hidden chaotic attractors. The simulated attractors are endorsed by the microcontroller execution of ASOOSS. Then, the total and partial controls of the amplitude of ASOOSS are demonstrated by using newly inserted parameters. Moreover, the efficacy of the configured single controller in suppressing chaos within ASOOSS is demonstrated through both analytical and numerical analyses. Furthermore, the binary data generated by the ASOOSS-based PRNG successfully passes the NIST 800–22 statistical tests, providing proof of the random nature of the ASOOSS-based PRNG and making it suitable for digital applications based on chaos. Additionally, controllers are devised to enable differential synchronization of three identical coupled chaotic ASOOSS systems. The effectiveness of the differential synchronization approach is validated through numerical simulations of the coupled chaotic ASOOSS systems.