The Analysis of Symmetrical Behavior for a Dual Flux-controlled Memristive Shinriki Oscillator Based on FPGA
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摘要: 该文通过将无源磁控忆阻器替换Shinriki振荡器中的二极管串并联支路，并利用有源磁控忆阻代替RLC谐振回路中的电阻，同时在电感支路串联电阻，得到一个新型双磁控忆阻Shinriki振荡器。通过特定参数的共存分岔图和Lyapunov指数谱，开创性地发现了振荡器具有的对称分岔行为，在双参数平面内展现运动状态分布的对称性。同时，在对称参数-初值平面的吸引盆中，分析对称域内系统的多稳态特性。并对存在的对称反单调现象、多运动状态吸引子对称共存和对称域中依赖初值的不完全对称行为进行研究。此外，基于FPGA技术完成双磁控忆阻Shinriki振荡器的数字电路实验，示波器上捕捉的波形验证了系统对称动力学行为分析的正确性。
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关键词:
- 双磁控忆阻Shinriki振荡器 /
- 对称动力学行为 /
- 多稳态特性 /
- 反单调性 /
- 不完全对称行为
Abstract: In this paper, a passive flux-controlled memristor is used to replace the diode series-parallel branch in the Shinriki oscillator, and the active flux-controlled memristor is introduced to substitute the resistance in the RLC resonant loop. At the same time, a series resistance is connected in the inductance branch to obtain a new type of dual flux-controlled memristive Shinriki oscillator. Through the coexisting bifurcation diagram of specific parameters and the Lyapunov exponential spectrum, the symmetric bifurcation behavior of oscillators is innovatively discovered, and the symmetry of the motion state distribution is shown in the two-parameter plane. Meanwhile, in the basin of attraction of the symmetrical parameter-initial value plane, the multistable characteristics of the system in the symmetrical domain are analyzed. The existence of symmetrical antimonotonic phenomena, the symmetrical coexistence of attractors with multiple motion states, and the incomplete symmetry behavior that depends on the initial value in the symmetric domain are studied. In addition, the digital circuit experiment of the dual flux-controlled memristive Shinriki oscillator is completed based on FPGA technology, and the waveform captured on the oscilloscope verifies the correctness of the system’s symmetrical dynamic behavior analysis. -
表 2 振荡器随参数c, d变化时的运动状态和对应Lyapunov指数
运动状态 Lyapunov指数 参数c <14.484 大周期 (0,–,–,–,–) (14.484,16.31)∪(16.684,18.928) 复杂运动(混沌，多周期) (+,0,–,–,–) (16.31,16.684)∪(18.928,23.68) 周期运动 (0,–,–,–,–) >23.68 稳定不动点 (–,–,–,–,–) 参数d <1.592 稳定不动点 (–,–,–,–,–) (1.592,1.804)∪(1.881,1.917) 周期运动 (0,–,–,–,–) (1.804,1.881)∪(1.917,2.038) 复杂运动(混沌，多周期) (+,0,–,–,–) >2.038 大周期 (0,–,–,–,–) 
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