类脑计算的基础元件：从忆阻元到分忆抗元

Basic elements of brain-like computing: From memristor to fracmemristor

摘要:

讨论一种新颖的类脑计算的基础元件：分忆抗元（分数阶忆阻元）.忆阻元的概念从经典的整数阶推广到分数阶忆阻元，即分忆抗元.分忆抗元是分数阶忆阻元的一个合成词.分忆抗值是分忆抗元的分数阶阻抗.因此，可以很自然地想到一系列具有挑战性的理论难题：分忆抗元和传统的分抗元以及著名的忆阻元的关系是什么；关于介于忆阻元和电容元或电导元之间的内插特性是什么；以及关于分忆抗元在蔡氏电路周期表中的位置在哪里；任意阶理想的容性分忆抗元和感性分忆抗元的分忆抗值的一般表达式是什么；分忆抗元的度量单位和物理量纲是什么；鉴别分忆抗元的指纹特征是什么；如何通过普通的忆阻和电容与电感以模拟电路形式有效实现任意分数阶忆阻元.基于大量的前期探索性研究成果，对上述一系列理论难题进行了初步探讨.分忆抗元解决了分抗元很难实现记忆端口电荷或磁通量的功能,而且分忆抗元可作为一种基本电路元件应用到混沌系统、神经元电路、神经网络电路等的设计.

Abstract:

In this paper, fractional-order memristor (fracmemristor), a novel basic element of brain-like computing, is discussed.The concept of memristor is extended from the conventional integer order to the fractional order, i.e. the fracmemristor. Fracmemristor is a compound word of fractional-order memristor, whose fractional impedance is fracmemristance. Accordingly, it is natural to think of a range of theoretical challenges: What is the relationship of fracmemristor to the conventional fractor and the famous memristor? What are the interpolation properties between the memristor and the capacitor or inductor? Where is the location of fracmemristor in the Chua's circuit periodic table? What are the general expressions for fracmemristances of arbitrary-order ideal capacitive and inductive fracmemristors? What are the measuring unit and physical dimensionality of fracmemristor? What are the fingerprint features for identifying fracmemristor? How to implement arbitrary fractional-order memristor effectively in the form of analog circuit with ordinary memristor, capacitor and inductor? This paper makes preliminary discussions on the above challenging theoretical problems based on abundant prior exploratory findings. The fracmemristor solves the problem that fractor is difficult to realize the function of memory charge or magnetic flux. As a basic circuit element, the fracmemristor can be applied to the design of chaotic system, neural circuit and neural network circuit.