This paper presents a new biophysical neuron model with double membranes, which incorporates two capacitors connected via a memristor, a smooth nonlinear resistor combined with an inductor, and a resistor. The model is designed to capture the flexibility and controllability of the cell membrane under external stimuli and noisy disturbance. The capacitive parameters are controlled by the energy diversity between capacitive fields under external stimuli and noisy disturbance. An energy function is obtained by applying scale transformation for the field energy, and coherence resonance is detected by applying noisy disturbance. The energy is expressed as a weighted function involving the membrane potential and channel currents, and the average energy value is effective to forecast the appearance of coherence resonance and neural activities become in high regularity. An adaptive criterion is suggested to explain how energy level for capacitive field can control the parameter shift due to energy injection and shape deformation on the cell membrane. When capacitive energy level is beyond a threshold, a parameter shift is induced to trigger suitable firing modes under external stimulus, and this property is effective to keep energy balance between adjacent neurons in the networks coexisting with multiple firing modes. Finally, entropy is estimated to discern the characteristic of firing modes. The most scientific significance is its physical description and approach of memristive membrane for cells. The paper also discusses the importance of considering energy level, energy shunting, controllability and coherence resonance under noise during information encoding and mode selection. The model is designed to better match the biophysical property of the cell membrane for a neuron, and the cell membranes show flexibility and shape deformation can be induced under continuous energy injection, physical stimuli. The paper concludes that introducing two capacitors into the neural circuit may be more suitable to match the biophysical property of the cell membrane for a neuron.This paper presents a new biophysical neuron model with double membranes, which incorporates two capacitors connected via a memristor, a smooth nonlinear resistor combined with an inductor, and a resistor. The model is designed to capture the flexibility and controllability of the cell membrane under external stimuli and noisy disturbance. The capacitive parameters are controlled by the energy diversity between capacitive fields under external stimuli and noisy disturbance. An energy function is obtained by applying scale transformation for the field energy, and coherence resonance is detected by applying noisy disturbance. The energy is expressed as a weighted function involving the membrane potential and channel currents, and the average energy value is effective to forecast the appearance of coherence resonance and neural activities become in high regularity. An adaptive criterion is suggested to explain how energy level for capacitive field can control the parameter shift due to energy injection and shape deformation on the cell membrane. When capacitive energy level is beyond a threshold, a parameter shift is induced to trigger suitable firing modes under external stimulus, and this property is effective to keep energy balance between adjacent neurons in the networks coexisting with multiple firing modes. Finally, entropy is estimated to discern the characteristic of firing modes. The most scientific significance is its physical description and approach of memristive membrane for cells. The paper also discusses the importance of considering energy level, energy shunting, controllability and coherence resonance under noise during information encoding and mode selection. The model is designed to better match the biophysical property of the cell membrane for a neuron, and the cell membranes show flexibility and shape deformation can be induced under continuous energy injection, physical stimuli. The paper concludes that introducing two capacitors into the neural circuit may be more suitable to match the biophysical property of the cell membrane for a neuron.