Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator

We study the dynamics of a resonantly driven nonlinear resonator (primary) that is nonlinearly coupled to non-resonantly linear (secondary) with relatively short decay time. Due its relaxation time, secondary adiabatically tracks primary and modifies response. Our model, which motivated by experimental studies on interaction between nano- micro-resonators, simple can be analyzed analytically numerically show response enhanced significantly due resonator. Such an arrangement may pave way for systematic control responses signal amplification in engineering applications involving micro-electro-mechanical-systems.