Dynamic Behavior Analysis In Memristor-based Switching Circuits

The memristor is the fourth primary circuit element which was discovered behind the resistors,capacitors and inductors.And the memristor means the relationship among the magnetic flow with the charge.By research,the memristor has the advantages of low power dissipation,nanometer size,easy integration and non-volatility.The nonlinear circuit based on memristor can generate very rich and complex dynamic behavior.At the same time,memristors have potential application value in many fields because of their unique non-linearity and memory characteristics.At present,most of the research on chaotic dynamics is based on smooth system.In recent years,it has been found that there are abundant nonlinear phenomena in switching circuits.In this paper,the memristor is combined with the switching circuit and its dynamic behavior is studied.The main work contents are as follows:(1)The mathematical model of the biquad Sigma Delta ADC modulator is established and use the Matlab for it to numerical simulation calculate.By analyze the graph of the sequence,the phases and the bifurcation of the system,it is found that there is chaos in the circuit system.The power spectrum diagram of the output signal of the circuit is drawn,and the performance of the ADC modulator circuit is analyzed.Then a second order Sigma Delta ADC modulator circuit based on the memristor is obtained by introducing the memristor into the modulator circuit.Similarly,this circuit is numerically simulated and analyzed by MATLAB simulation software,and it is found that the second-order Sigma Delta ADC modulator circuit based on the MEMSTOR has higher signal-to-noise ratio and better modulator accuracy.(2)A kind of switch circuit based on memristor is constructed,and three working modes of the circuit are particular introduced,and the corresponding mathematical was build for them.There are multiple attractor bifurcations in this circuit,and when the boundary collision occurs,different attractors coexist in the system.These include the coexistence of single periodic limit cycles and chaotic attractors,different chaotic attractors,symmetric 2-periodic limit cycles,symmetric2-periodic limit cycles and 5-periodic limit cycles,etc.Finally By combining the graph of the phases and the bifurcation to analyze the kinetic behavior of this circuit.By use the PSIM circuit to prove the validity of the numerical calculus.The proposed circuit is of great significance to the study of the coexistence of multiple attractors and the application of chaos in switching circuits.