中文摘要：

忆阻器是一种新型的非线性动态可变电阻器，其阻值的变化依赖于通过它的电荷量或磁通量。作为第四种基本电路元器件，忆阻器在非易失性存储器、非线性电路及系统、神经形态系统等领域中有巨大的应用潜能。忆阻器串并联组合电路具有比单个忆阻器更为丰富的器件特性，引起了研究者越来越多的关注。本文推导了带有窗函数的闭合形式的电荷及磁通量控制的忆阻器非线性模型，能够有效地模拟忆阻器边缘附近的非线性离子迁移现象，同时保证忆阻器的边界条件。进一步，分别从忆阻器的器件参数和激励阈值两个角度，对忆阻器串并联电路进行了全面的理论推导和数值分析。为了更加直观地观察忆阻器串并联特性，设计了一种基于Matlab的忆阻器串并联图形用户界面，能够清晰地展示两种分类方式下忆阻系统的器件特性，可为忆阻器组合电路的后续研究提供良好的理论参考和实验依据。

英文摘要：

The memristor is a novel kind of electronic device with dynamic variable resistance that is dependent on the past history of the input current or voltage. As the fourth fundamental circuit element, the memristor captures a number of unique properties that have been found to possess attractive potentials in some promising fields such as nonvolatile memory, nonlinear circuit and system, and neuromorphic system. Additionally, compared with a circuit of single memristor, series-parallel circuit of memristors possesses more abundant device characteristics which arouses increasingly extensive interest from numerous researchers. In this paper, the mathematical closed-form charge-governed and flux-governed HP memristor nonlinear models are presented with constructive procedures. In particular, these models are more realistic by taking into account the nonlinear dopant drift effect nearby the terminals and the boundary conditions, and by adding a simple and effective window function. Furthermore, based on the internal parameters and threshold of the memristor respectively, the theoretical derivation and numerical analysis of the memristor-based series-parallel connection circuits have been made comprehensively. For obtaining the characteristics of the memristor-based combinational circuits intuitively, a graphical user interface is designed based on Matlab software, which is beneficial to displaying the properties of the memristive system clearly. The results in the present paper may provide theoretical reference and reliable experimental basis for the further development of the memristor-based combinational circuits.