Nonlinear Resonance in a Position-Dependent Mass-Duffing Oscillator System with Monostable Potentials Driven by an Amplitude-Modulated Signal

Abstract

This study examines the phenomenon of vibrational resonance (VR) in a classical positiondependent mass (PDM) system characterized by three types of single-well potentials. These potentials are influenced by an amplitude-modulated (AM) signal with $\Omega\gg\omega$. Our analysis is limited to the following parametric choices:
(i) $\omega_0^2$, $\beta$, $m_0$, $\lambda>0$ (type-1 single-well),
(ii) $\omega_0^2>0$, $\beta <0$, $2< m_0 <3$, $1< \lambda <2$ (type-2 single-well),
(iii) $\omega_0^2>0$, $\beta <0$, $0< m_0 <2$, $0<\lambda<1$ (type-3 single-well).
The system presents an intriguing scenario in which the PDM function significantly contributes to the occurrence of VR. In addition to the analytical derivation of the equation for slow motions of the system based on the high-frequency signal’s parameters using the method of direct separation of motion, numerical evidence is presented for VR and its basic dynamical behaviors are investigated. Based on the findings presented in this paper, the weak low-frequency signal within the single-well PDM system can be either attenuated or amplified by manipulating PDM parameters, such as mass amplitude ($m_0$) and mass spatial nonlinearity $\lambda$. The outcomes of the analytical investigations are validated and further supported through numerical simulations.