双忆阻Shinriki振荡器的超级多稳态和反单调性分析

本文通过在Shinriki振荡器中引入一个有源荷控忆阻，并且利用一个含绝对值项的磁控忆阻代替原电路中的串并联二极管回路，提出了一种含双忆阻器的Shinriki振荡器.根据电路拓扑结构图建立了忆阻振荡器的数学模型，开展了振荡器随电路元件参数变化时的共存分岔、周期-混沌状态转移等动力学特性分析.结果表明，双忆阻Shinriki振荡器对忆阻的参数值和初始条件有极大的依赖性，随着忆阻参数值和初始条件在特定域内变化，振荡器将呈现出共存反单调现象、不完全对称行为、超级多稳态等非线性动力学行为.此外，基于FPGA开发板完成了双忆阻Shinriki振荡器的数字电路仿真，在示波器上捕捉实验波形，验证了动力学分析的正确性.

The Analysis of Antimonotonicity and Extreme Multistability for a Two-Memristor-Based Shinriki Oscillator

A dual memristive shinriki oscillator is proposed through expanding Shinriki oscillator with an active charge-controlled memristor and substituting the series-parallel diode loop in the original circuit with a flux-controlled memristor with an absolute value term.Firstly,the mathematical model of the memristive oscillator is established according to the circuit topology diagram.Secondly,the coexisting bifurcations and routes to period-chaos transitions are analyzed when the circuit parameters are changed.Results show that Shinriki oscillator with double memristors exhibits a great dependence on parameter values and initial conditions of memristors.When the parameter values and initial conditions vary in a particular domain,the oscillator will exhibit nonlinear dynamical behaviors such as the phenomenon of coexisting antimonotonicity,incomplete symmetric behaviors,extreme multistability,etc.Moreover,the digital module circuit of the oscillator is constructed by the FPGA development board.The experimental waveform is captured on the oscilloscope,which verifies the accuracy of numerical simulation.