Crisis-Induced Vibrational Resonance in a Phase-Modulated Periodic Structure New Submission

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation.  We employed theoretical analysis using the separation of motions approach and 4th order Runge-Kutta numerical simulation in MATLAB to characterise the system's response. We identified two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyse these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

Through bifurcation analysis, Poincaré sections, and phase portraits, we revealed an attractor-merging crisis where two coexisting periodic attractor branches merge into a single quasiperiodic orbit when phase modulation amplitude exceeds a critical threshold. This transition substantially enlarges the basin of attraction and amplifies system response, a mechanism not previously reported for vibrational resonance induction, with significant implications for superconducting electronics, quantum computing, secure communications, quantum sensing, and energy harvesting applications.