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Control of Energy Flow from Branch Circuit and Synchronization between Neural Circuits

  • Xiangxiao Du 1,   
  • Zhao Lei 2,*

Received: 17 Aug 2026 | Revised: 09 Sep 2026 | Accepted: 17 Sep 2026 | Published: 23 Sep 2026

Abstract

Neural firing activity is fundamentally governed by the nonlinear coupling between electric field energy and magnetic field energy in neural circuits, and the introduction of different ion channel shunting devices (capacitor, inductor, memristor) enables energy shunting (redistribution), thereby achieving modulation of firing patterns. In this paper, a neuronal circuit model with rich firing modalities is constructed by incorporating a nonharmonic excitation source (a voltage source in series with a nonlinear resistor) and an ion channel shunting mechanism. We systematically examine the effects of shunting control on neuronal firing and synchronization from three aspects: nonlinear dynamics, Hamilton energy response, and coupling-modulated synchronization. The results show that both internal parameters and external excitations effectively modulate firing patterns, with different parameters exhibiting distinct energy‑regulation trends. Moderate noise optimize firing regularity and promote energy accumulation via stochastic resonance (SR). An energy-based adaptive control strategy is further introduced, which actively steers the system between among dynamical regimes, confirming energy as a valid criterion for state regulation. For synchronization, we construct multiple coupling strategies are constructed using three coupling elements and two coupling topologies. The results consistently show that complete synchronization is achievable across all strategies; however, the shunting coupling consistently requires higher critical coupling strengths, implying richer regulatory flexibility at the expense of higher coupling intensity. These findings systematically elucidate the regulatory mechanisms of ion channel shunting on neuronal firing and synchronization, and provide theoretical guidance for energy-efficient optimization and synchronization-control design in neuromorphic circuits.

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Du, X.; Lei, Z. Control of Energy Flow from Branch Circuit and Synchronization between Neural Circuits. Physical Models and Application 1.
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