Dynamics of a functional neural circuit without capacitor embedding

In this paper, a novel functional neural circuit model is proposed without embedding capacitors in the branch circuit, and the setting breaks the design limitation of traditional capacitor-based neural circuits. By replacing the capacitor with a charge-controlled memristor (CCM) for electric field energy storage and coupling a Josephson junction with a thermistor, the circuit achieves multi-physics field sensing capability for both external electromagnetic fields and temperature signals. Based on Kirchhoff's law and Helmholtz's theorem, we derive the dimensionless theoretical model from circuit equations and an exact Hamilton energy function is confirmed. We also systematically investigate how the critical current of the Josephson junction, the switching rate of the ion channel, and the ambient temperature modulate the neural firing patterns. Our results indicate that the circuit can intermittently switch between multiple modes-including periodic, bursting, and chaotic firing-and exhibits distinct output signal characteristics: the chaotic state is characterized by high amplitudes and low frequencies, whereas the periodic state is characterized by low amplitudes and high frequencies. Furthermore, the model shows a clear stochastic resonance phenomenon under Gaussian white noise perturbation, with increasing temperature lowering the noise intensity threshold required to induce stochastic resonance. These findings not only validate the biological plausibility and functional reliability of capacitorless neural circuits, but also provide novel design insights and engineering strategies for the development of highly integrated neuromorphic devices and intelligent sensor systems.