Controlling neural activity by shunting channel current in a memristive FitzHugh-Nagumo circuit

Membrane potential is an observable output, whereas the ion channel pathway governs the internal current partitioning that shapes neural firing modes. Here, we construct a memristive FitzHugh-Nagumo neural circuit in which a tunable diversion branch is connected to the canonical ion channel branch, enabling the regulation of neural firing through the controlled redistribution of channel current. Physical implementation of this strategy is verified by incorporating different electric elements in the sub-branch circuit: (i) a shunting capacitor for differential-type diversion and (ii) a shunting inductor in series with a protective resistor for integral-type diversion. For the two controlled circuits, physical equations and field energy functions are derived, and the corresponding theoretical models and corresponding energy functions are obtained and further checked by the Helmholtz theorem. Numerical analysis shows that capacitive shunting can trigger an abrupt collapse of the inductive energy level in L1 and thereby induce firing-mode transitions, whereas inductive shunting produces markedly weaker modulation over comparable parameter ranges. The model also exhibits noise-induced stochastic resonance, and an adaptive energy-guided regulation law controls the electrical activities effectively. The results suggest that control of firing patterns depends on the physical property of the shunting element and provide a physically interpretable strategy for ion-channel-level regulation in memristive neural circuits.