Self-Excited and Hidden Attractors in an Autonomous Josephson Jerk Oscillator: Analysis and Its Application to Text Encryption

Abstract

By converting the resistive capacitive shunted junction model to a jerk oscillator, an autonomous chaotic Josephson jerk oscillator which can belong to oscillators with hidden and self-excited attractors is designed. The proposed autonomous Josephson jerk oscillator has two or no equilibrium points depending on DC bias current. The stability analysis of the two equilibrium points shows that one of the equilibrium points is unstable while for the other equilibrium point, the existence of a Hopf bifurcation is established. The dynamical behavior of autonomous Josephson jerk oscillator is analyzed by using standard tools of nonlinear analysis. For a suitable choice of the parameters, an autonomous Josephson jerk oscillator can generate antimonotonicity, periodic oscillations, self-excited chaotic attractors, hidden chaotic attractors, hidden chaotic bubble attractors, and coexistence between periodic and chaotic self-excited attractors. Finally, a text cryptographic encryption scheme with the help of generalized function projective synchronization of the proposed autonomous Josephson jerk oscillators in hidden chaotic attractor regime is illustrated through a numerical example, showing that a high-level security device can be produced using this system.