具有突触特性忆阻模型的改进与模型经验学习特性机理

许多忆阻器都具有与生物神经突触功能相似的特性,这些特性包括记忆与遗忘特性、经验学习特性等.文献[17]根据记忆与遗忘特性建立了这类忆阻器的模型,文献[19,20]在对该模型的仿真研究中发现该模型也具有描述经验学习特性的能力.在关于这一模型已有研究的基础上,本文对该模型状态方程的特性与机理给出进一步的分析.分析中发现原模型的窗口函数的设计和使用存在问题,并且原模型建模时对于实验现象的解读不够准确.针对这些问题对原模型的状态方程进行了改进,完善了模型功能.对于该模型能够描述经验学习特性的机理,分别利用对于模型的状态方程的分析以及周期脉冲信号作用下的状态方程解析分析,对该机理给出定性和定量的讨论.利用机理分析所得的相关结论,设计了基于经验学习实验的模型状态方程中的参数和函数的估计方法,方便了该模型在这一类忆阻器的实验研究中的应用.

Modification of memristor model with synaptic characteristics and mechanism analysis of the model's learning-experience behavior

Many memristors fabricated by different materials share the characteristics which are similar to the memory and learning functions of synapse in biological systems. These characteristics include memorizing and forgetting function and learning-experience behavior. A memristor model was proposed in the published paper [Chen L, Li C D, Huang T W, Chen Y R, Wen S P, Qi J T 2013 Phys. Lett. A 377 3260] to describe the memorizing and forgetting function of this kind of memristor. This model includes three state variables ω, τ and ε. The change of w describes the variation of the conductance of the memristor, a function f_E (·) is used to the input voltage's influence on the change of ω, τ and ε are used to describe the its forgetting effect. The simulation analyses of this model in the published papers [Chen L, Li C D, Huang T W, Hu X F, Chen Y R 2016 Neurocomputing 171 1637] and [Meng F Y, Duan S K, Wang L D, Hu X F, Dong Z K 2015 Acta Phys. Sin. 64 148501] showed that this model can also describe the learning-experience behavior. This model is further studied in this paper to show its detailed characteristics. The analyses of the state equations of the original model show that these state equations cannot restrict the state variables in their permissible interval because the window function is not appropriately used in all the state equations, and the original window function cannot force the state equation to be identical to zero either when corresponding state variable reaches its bound. An improved window function is introduced and the appropriate utilization of this window function is discussed to deal with this problem. The upper bound of τ is defined in the modified model to describe the saturation of τ that has been observed in the experimental studies of this kind of memristor. The behaviors of the modified state equations are different from those of the original ones only when the state variables reach their bounds, and this modified model has the same ability to describe the memristor's memorizing and forgetting function and learning-experience behavior as original one. The behaviors of the model when the input voltage is not negative are discussed based on the state equations and their analytical solution when the input is the repeated voltage pulses, and the results of the discussion are used to explain how a model designed according to the memorizing and forgetting function can also describe the learning-experience behavior. The analysis shows that the increased rising speed of the state variable w in the stimulating process is caused by increasing the values of τ and ε, and the learning-experience behavior described by this model would also be influenced by the value of τ:a smaller initial value of state variable τ in the learning-experience experiment would lead to a more obvious learning-experience behavior. The analytical results are also used to design an estimation method based on the learning-experience experiment to estimate the parameters and function in the state equation. The further discussion shows that this proposed estimation method can also be used to verify the reasonability of the assumption used in the state equations that the derivatives of τ and ε are proportional to f_E (V).