From a neural circuit to a biophysical neuron model, standard scale transformation requires the combination of physical variables including capacitance and resistance associated with a capacitor C and a resistor R, respectively. The voltage across the capacitor is used to mimic the membrane potential for neurons. Therefore, most of the neuron models contain one or two capacitive variables for the membrane potential. In fact, the reference time scale (RC) can be replaced by combinating parameters for inductor and resistor during approach of scale transformation for physical variables in the neural circuit. In this study, a simple nonlinear circuit is built by applying two inductors, a charge-controlled memristor (CCM), a nonlinear resistor and a resistor. The circuit equations are derived to develop a memristive oscillator with exact description of energy function. Furthermore, an equiavlent memristive map is obtained by applying linear transformation on the sampled variables from the memristive oscillator. The Hamilton energy function for memristive oscillator is calculated by using the Helmholtz's theorem, and then the memristive map is given in energy function in discrete form. The memristive map has rich dynamic characteristics and can identify coherence resonance under applying noisy electric field. This scheme will provide a theoretical guidance for building nonlinear circuits and maps without using capacitors.