Energy consumption analysis and logical stochastic resonance of Memcapacitor Hodgkin–Huxley neuron based on the Miller effect

This study innovatively introduces a memcapacitor based on the Miller effect into the classical Hodgkin–Huxley (HH) neuron system, proposing an improved Memcapacitor Hodgkin–Huxley (MC–HH) neuron model. By replacing the traditional membrane capacitance with a memcapacitive element, this model fully leverages the unique memory characteristics of the memcapacitor, significantly enhancing the model's dynamic behavior and its simulation capability for the history-dependent properties of biological neurons. During the research process, nonlinear dynamic analysis methods such as bifurcation diagrams and phase trajectory plots were employed to investigate the complex dynamic behaviors of the model under the influence of the memcapacitor, as well as the logical stochastic resonance phenomenon driven by Gaussian white noise. The results indicate that the model exhibits bistability and hysteresis phenomena, revealing the "trigger flux – membrane capacitance – electrical activity – energy metabolism" mechanism through the synergistic regulation of stimulus current and trigger flux. Furthermore, this model not only inherits the advantage of classical HH neurons in achieving reliable logical operations but also provides a new regulatory dimension for the logical design of neuromorphic computing by leveraging the unique memory characteristics of the memcapacitor, which holds promise for advancing the development of highly integrated neuromorphic chips.