Abstract: This study proposes a novel control method for neuronal circuits based on targeted parallel shunting using an external capacitor. A hybrid circuit integrating a memristor, a Josephson junction, and a nonlinear resistor is constructed, with an external capacitive branch introduced in parallel with the nonlinear resistor to achieve precise manipulation of neuronal firing patterns. It is demonstrated that the external capacitive branch enables effective regulation of the firing patterns of the neuronal circuit through its targeted parallel connection to the nonlinear resistor. By continuously adjusting the external capacitance parameter, the system can realize controllable switching among various firing modes. Concurrently, variations in the stimulus amplitude reshape the internal energy distribution framework of the system, determining the dominant roles of different energy storage components. These two mechanisms constitute a dual-dimensional "mode-energy" regulation system for the neuronal circuit. Furthermore, the regulatory mechanism of the external branch originates from its unique local shunting effect and specific energy exchange process. The energy evolution of the external capacitor exhibits dynamic characteristics distinct from those of the main system, and this asynchronous energy response can effectively perturb the global balance of the system. The proposed method provides a foundation for the precise control of neuronal dynamics in memristive Josephson systems.

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