actuation, the potential energy of the oscillator is asymmetric about the equilibrium position and has the form V ( z ) = 1 $_{2}$K$_{eff}$ z $^{2}$+ θz $^{3}$+ µz $^{4}$+ H.O. ( z ), where K$_{eff}$ , θ and µ are coefficients depending on V DC g . We have experimentally probed the non-linear and hysteretic response of the device. Fig.5a, 5b, 5c, and 5d, show the experimentally measured non-linear response of this device leading to hysteretic behavior as function of V DC g with increasing amplitude of driving force. Here, V DC g is swept at a given drive frequency to measure the mixing current and several such V DC g sweeps are collated (the distinct response of sweeping the frequency at a fixed V DC g – a common mode to study non-linear response – is described in supporting information). There are two features that we would like to point out – first, in the region at the bottom of the W-shaped dispersion curve, two branches of the same mode merge into one broad peak where the oscillator has large amplitude over a wide range of V DC g and second, whenever during the V DC g sweep, one crosses the region with a local negative value for df 0 dV DC g (here, f$_{0}$ is the resonant frequency at a particular V DC g ), shows a curved hysteretic j -shaped response (indicated by ⋆ ), seen in Fig.5b. In order to understand and explain the experimentally observed hysteretic response as a function of V DC g , we have used the Duffing equation [40] for our resonator. The result of such a calculation for amplitude is seen in Fig.5e, 5f, 5g, and 5h, with increasing amplitude of driving force. To calculate the amplitude we have only used the observed dispersion relation (W shape) as input for Duffing equation. There is a qualitative agreement between the experimentally measured data shown in Fig.5a- d and results of calculation using the Duffing equation shown in Fig.5e-h. We find that for every increase in excitation amplitude by 100 mV corresponds to an increase of a factor of 2.5 in the anharmonic component of the Duffing equation (from observing the calculated data). Additional aspect of the nonlinearity of the oscillator is also seen in the evolution of dispersion near V DC g = 0 as the actuation amplitude is gradually increased from 100 mV to 400 mV in Fig.5a-d. The negative dispersion is due to the softening of electrostatic force and with larger amplitude of oscillation the effective spring constant changes, as the wire samples a region with varying electric field; this difference is clearly seen in the dispersion near V DC g = 0 for the data shown in Fig.5 a and d. Fig.5i, shows the line plot (along the dashed line in Fig.5f) of calculated amplitude for different sweep direction of V DC g and the resulting hysteresis. The observed hysteretic response, as a function of V DC g , is quite different from the hysteretic response as a function of drive frequency ( discussed in supporting information ). This non-linear response of our 8