自适应突触神经元简化模型的动力学与电路实现

Dynamics and Circuit Implementation of a Simplified Model of Adaptive Synaptic Neuron

自适应突触神经元模型具有两个复杂激活函数,导致其不易于理论分析和硬件电路实现.然而,该神经元的主要放电活动仅受到两个激活函数的局部曲线特征的影响,且这些局部曲线特征是完全不一样的.鉴于此,采用两个简单函数分别对两个不同局部曲线特征进行拟合,提出了一种自适应突触神经元的简化数学模型.基于平衡点轨迹图,阐述了该简化模型随外部刺激变化的平衡点稳定性演化机理,它经由Hopf分岔实现稳定与不稳定平衡态之间转迁.借助理论分析和数值仿真,分析了不同参数下自适应突触神经元的复杂动力学.最后,采用分立元器件进行了模拟电路设计,制作印刷电路板,由数字示波器捕捉的运动轨迹图,验证了简化激活函数的可行性与MATLAB数值仿真的正确性.

Adaptive synaptic neuron model has two complex activation functions,which make it difficult to be analyzed theoretically and implemented in hardware circuit.However,the main firing activities of this neuron are only affected by the local curve characteristics of the two activation functions and these local curve characteristics are completely different.In view of this,a simplified mathematical model of adaptive synaptic neuron is proposed using two simple functions to respectively fit the two different local curve characteristics.Based on the trajectory diagram of the equilibrium point,the evolution mechanism of the equilibrium stability of the simplified model with the change of external stimulus is explained.It achieves the transition between the stable and unstable equilibrium states via Hopf bifurcation.By means of theoretical analyses and numerical simulations,complex dynamics of the adaptive synaptic neuron under different parameters is investigated.Finally,an analog circuit is designed using discrete components and a printed circuit board is made.The motion trajectory captured by a digital oscilloscope verifies the feasibility of the simplified activation functions and the correctness of MATLAB numerical simulations.