The Analysis Of Nonlinear Circuit Characteristic Based On Memory Elements

Memory elements are the components that have memory characteristics, including the memristor, memcapacitor and meminductor. These three components are non-linear device and their state depended on their historical status. The current-voltage curve of memristor, charge-voltage curve of memcapacitor and current-flux curve of meminductor are typically pinched loops under sinusoidal input signal. Due to the unique nature of the memory element, they are widely used in solid storage, artificial neural networks, nonlinear science and other areas.In this paper, we studied the nonlinear circuit based on memory element. The main contents of this paper include the following sections:1. According to the principle of the memristor, we build the second-order and third-order memristor analog circuits. And on this basis, the second-order and third-order memristor analog circuits were converted into the corresponding second-order and third-order memcapacitor analog circuits. Simulation and experimental results showed that the obtained memristor and memcapacitor with a sinusoidal input signal were hysteresis characteristic, which is consistent with the nature of the memristor.2. The filtering characteristics of the RC low-pass filter circuit based on second-order memcapacitor was studied in this paper. The simulation and experimental results showed that the low frequency signal could get through the circuit low-frequency, however, the high-frequency signal was suppressed. In addition, compared to the conventional RC low-pass filter circuit, the low-pass filter circuit based on second-order memcapacitor had variable cut-off frequency.3. A new Duffing-van der Pol oscillator circuit based on memristor was proposed. The homoclinic orbits equation of undisturbed system were analyzed and based on this Melnikov function of the system was deduced when there are disturbances. The chaotic conditions of the system accounted for the iterated effect of the Smale horseshoe map was analyzed by Melnikov function. Numerical simulation results showed that limit cycle and apparent chaotic phenomenon were observed in this system. Meanwhile, the same phenomenon was confirmed by Lyapunov exponent and bifurcation diagram of the system. On the other hand, chaotic motion can be observed by Multisim software simulation.