Energy Dynamics and Circuit Implementation for a Neuron with a Memcapacitive Membrane

The output voltages for the capacitive elements of a neural circuit model can be mapped into dimensionless capacitive variables, which present firing patterns similar to the membrane potentials detected in biological neurons. The inclusion of a memcapacitor also enables consideration of membrane deformation effects, enhancing the model's capacity to simulate neuronal behavior across varying physiological and environmental conditions. In this study, a capacitor and a memcapacitor are connected through a linear resistor in parallel with other electric components in different branch circuits composed of an inductor and a nonlinear resistor. The electrical activities in a neuron with a double-layer membrane and two capacitive variables are discussed in detail after converting the nonlinear equations for the neural circuit into a theoretical neuron model. A dimensionless neuron model and its corresponding energy function are derived. The field energy function for the neural circuit is converted into an equivalent Hamilton energy function and further validated via the Helmholtz theorem. Furthermore, the average value of energy serves as an indicator for predicting stochastic resonance, as supported by analyzing the distribution of the coefficient of variation. The neuronal firing patterns are shown to be energy-dependent. An adaptive control strategy is proposed to regulate mode transitions in electrical activities of the neuron. An analog equivalent circuit is constructed to experimentally verify the numerical results, thereby supporting the reliability of the proposed neuron model.