中文摘要：

忆阻器是纳米级器件,其功耗低,集成度高,有着巨大的应用潜能.单个器件具有丰富的电学性质,其串并联电路更展现了丰富的动力学行为.然而,忆阻器在高密度集成的环境下,其耦合效应不可忽视.因此,本文首先基于磁控忆阻器推导了耦合忆阻器的数学模型.其次,在考虑不同极性连接和耦合强度的前提下,讨论两个磁控忆阻器串并联的耦合情况,进行了详细的理论分析,并通过数值仿真探索了耦合效应对忆阻系统的影响.同时,设计了基于Matlab的图形用户界面,直观地展示了不同参数下的耦合特性曲线.进一步,本文展示了有无耦合情况下,初始阻值对忆阻器正常工作范围的影响.最后,构建耦合忆阻器的Pspice仿真器,从电路的角度再次验证了忆阻器间的耦合效应.实验结果表明：同极性耦合增强了阻值的改变,相反极性的耦合减缓了阻值的改变.这些动力学特性可以很好地应用于忆阻网络中,也为全面考虑忆阻系统电路的设计提供了强大的理论基础.

英文摘要：

Memristor is a nanoscale element with low power consumption and high integration,having great potential in applications.A single memristor has rich electrical properties,and its series-parallel circuit exhibits more abundant dynamic behaviors.However,memristors’ coupled effects cannot be ignored in high-density integrated environment.Therefore,this paper first deduces the mathematical model of coupled memristor in detail based on the coupled flux controlled memristors.Second,considering the different polarity connection and coupling strength,we discuss the coupled condition of two flux-controlled memristors in series and parallel connections.Then the detailed theoretical analysis is illustrated,and the variation of memristance in terms of voltage,time and flux as well as the relations between voltage and currents are examined via numerical simulations to further explore the influence of coupled effects on the memristive system.At the same time,a graphical user interface of series-parallel coupled circuit based on Matlab is designed.Through this interface,we can adjust the initial value of memristor and coupling coefficient,select different connection modes,obtain corresponding connection diagram and output waveform which intuitively show the dynamic behavior of different parameters directly and provide experimental reference for further study of the circuit design.Furthermore,this paper shows the influence of initial value on the normal working range of memristors in the presence of coupling.From the table 1 it can be easily obtained that when the memristors are connected in the same direction,the range of memristance without coupling is greater than that with coupling.And the situation is opposite when the memristors are connected in different directions.Finally,the hysteresis curve with different coupling coefficients and the change of memristance with time are shown via building the Pspice simulator of coupled memristors,so the coupling effects of memristor is confirmed by circuit simulations.Experimental re