A double–membrane neuron and circuit containing a memcapacitor

This study focuses on the changes in the outer membrane characteristics of double–membrane neurons under external stimuli, and proposes a neural circuit model based on the combination of memcapacitors and memristors. This model can precisely describe the dynamic changes in the cell outer membrane capacitance due to stretching or compression without the need for inductance elements. The M2 memristor introduced in the model not only expands the input signal frequency band but also enhances the effect of the outer membrane ion channels. By paralleling linear resistor, capacitor, and memcapacitors, and ingeniously adding two memristors to the circuit, a tunable coupled neuron with a strict Hamilton energy function is constructed. Bifurcation theory and energy–firing behavior correlation analysis reveal the rich firing dynamics of the neuron, and a method for detecting biological heat using Tp is proposed. At the same time, the system thoroughly examines the effect of external fields, finding that a moderate external field can induce new firing patterns, while an overly strong external field leads to the disappearance of the dynamical bifurcation, and random external fields result in the observation of stochastic resonance (SR). Additionally, the model adopts an adaptive control criterion to effectively regulate the energy flow and output activities. The capacitance ratio and gain parameters determine the degree of chaos and control speed of neural firing. The results of this study provide theoretical support and new ideas for the design of functional neural circuits without inductance elements, and lay the foundation for subsequent construction of more efficient neural functions through the linking of capacitors with nonlinear resistors or memristors.