• A memcapacitor-based neuron model with two capacitive variables is developed to simulate membrane deformation and double-layer membrane effects.
• The field energy of the neural circuit is converted into a Hamilton energy function and validated via the Helmholtz theorem.
• The average energy value is shown to predict coherence/stochastic resonance, supported by coefficient-of-variation analysis.
• An adaptive control strategy and analog equivalent circuit confirm energy-dependent firing-pattern transitions and model reliability.