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 results reflect that the coupling with the same polarity enhances the change of resistance, and the coupling with different polarity with slow down it. Such dynamical properties can be well utilized in memristive networks and provide a strong theoretical basis for the comprehensive consideration of the design of memristive system.
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