Abstract

This paper presents a numerical investigation of subthreshold signal enhancement in a Van der Pol-Duffing oscillator through the phenomenon of Vibrational Resonance. The oscillator models the motion of a particle in a muti-stable periodic potential, influenced by a space-dependent nonlinear damping and driven by an external bichromatic excitation. Temporal and spectral analyses methods were applied to examine the system’s response. The results show that the low-frequency input signal 2|X(f_Lf )| is amplified from 0.03316 to 0.1787 when the amplitude of the high-frequency perturbation is adjusted from G=50 to an intermediate value G=430 respectively. This finding is further supported by the linear response analyses for fixed damping amplitude γ=0.06. Additionally, the damping amplitudes were found to influence the system's behavior, with the optimal linear responses, Q=1.787 and Q=1.869, occurring at damping amplitude values of γ=0.04 and h=1.5 respectively.

Key words: Subthreshold signal, signal enhancement, van der Pol-Duffing oscillator, multi-stability space-dependent damping, Vibrational Resonance