关键词: memristive neuron, dynamical behaviors, LTspice simulation

Abstract: The physical circuit model of biological neurons can be obtained by applying electronic components to simulate the ion channels and membrane potential of biological neurons. The effective physical circuit model of neurons provides an experimentally verifiable physical carrier for understanding the information encoding mechanism of the nervous system. In addition, the nonlinear dynamic characteristics of the physical circuit model of the neuron lay the bionic foundation for brain-inspired computing and the design of low-power neuromorphic chips. Therefore, this paper designs a dual-capacitor memristive neural circuit without any inductive elements and analyzes the nonlinear dynamic characteristics of the physical circuit model of the neuron. First, Kirchhoff's current law is applied to derive the differential equations describing the memristive neural circuit, and a neural dynamics model expressed by the differential equations is established. The corresponding energy function of the memristive neural circuit is derived based on Helmholtz's theorem. Subsequently, nonlinear dynamical analysis methods are employed to investigate the complex dynamical behaviors of this neural model. The results indicate that the electrical activity of the neuron can be effectively modulated by external stimuli and external magnetic fields; specifically, this neuron model exhibits stochastic resonance phenomena under a noisy magnetic field. Furthermore, the neuron's self-regulatory capability is verified using an adaptive method based on energy ratio control. The hardware feasibility of this neuronal model is further validated through LTspice simulation. Finally, this neuronal model can be coupled to form a neural network for investigating the collective behaviors of neural networks and the influence of external magnetic fields on their collective properties.

Key words: memristive neuron, dynamical behaviors, LTspice simulation