Exploring sensitive vibrational resonance in coupled bistable oscillators
摘要
We study the phenomenon of sensitive vibrational resonance in driven coupled bistable Duffing oscillators under both non-diffusive and diffusive coupling schemes. By analyzing the system’s response with varying high-frequency force amplitude (g), we uncover distinct vibrational behaviors in the slow and fast variable oscillators. The resonance peaks and response amplitudes are shown to depend strongly on initial states of the system with multistable vibrational states emerging within specific parameter regions. These states are highly sensitive to initial conditions, enabling tunable dynamics and switching behavior between maximal, zero, and limiting responses. We report the emergence of a novel hysteresis loop in both fast and slow variable oscillators, where the system’s response depends on initial conditions and its dynamical history. As the parameter g increases, the system exhibits resonance behavior, whereas decreasing g results in a constant response that remains largely independent of g within the hysteresis regime. This phenomenon occurs across both coupling schemes examined. The observed sensitive vibrational resonance properties have potential implications for applications requiring precise control of signal amplification, filtering, or dynamic switching, such as in neural signal processing, mechanical sensing, vibration isolation, and secure communication systems.