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To address the issues of high dynamic power consumption and substantial occupation of silicon integration resources in traditional capacitor-containing neuronal circuits, this study proposes a capacitor-free neuronal circuit based on a charge-controlled memristor. By taking the intrinsic parameters of the charge-controlled memristor as the reference for scaling transformation, dimensionless dynamical equations were derived. The local asymptotic stability of the system was verified using Jacobian matrix eigenvalue decomposition and the Routh-Hurwitz criterion. Gaussian white noise was introduced to simulate interference for detecting coherent resonance, while energy characteristics were analyzed by combining Hamiltonian energy formulas and resistance energy consumption expressions. Additionally, the fourth-order Runge-Kutta method was employed to conduct numerical simulations.
The research results indicate that external stimuli, ionic channel conductance, and reversal potential can flexibly regulate the periodic/chaotic firing modes of the neuron. In the periodic state, the proportion of electric field energy of the charge-controlled memristor in the total energy is higher; in the chaotic state, however, the proportion of magnetic field energy of the inductive coils increases. The circuit exhibits coherent resonance under the influence of noise, and resistor is the main energy-consuming component. The conclusion confirms that the circuit is feasible in principle, with rich dynamical characteristics and good noise robustness. Changing the resistance value can improve energy efficiency while retaining multiple firing modes, which provides theoretical support and an optimization direction for the design of high-integration, low-power neuromorphic computing circuits.-
Keywords:
- Memristive neural circuits /
- Stability analysis /
- Coherent resonance /
- Energy consumption control
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