School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China.
Chaos. 2023 Feb;33(2):023122. doi: 10.1063/5.0126900.
In this paper, the complex routes to chaos in a memristor-based Shinriki circuit are discussed semi-analytically via the discrete implicit mapping method. The bifurcation trees of period-m (m = 1, 2, 4 and 3, 6) motions with varying system parameters are accurately presented through discrete nodes. The corresponding critical values of bifurcation points are obtained by period-double bifurcation, saddle-node bifurcation, and Neimark bifurcation, which can be determined by the global view of eigenvalues analysis. Unstable periodic orbits are compared with the stable ones obtained by numerical methods that can reveal the process of convergence. The basins of attractors are also employed to analyze the coexistence of asymmetric stable periodic motions. Furthermore, hardware experiments are designed via Field Programmable Gate Array to verify the analysis model. As expected, an evolution of periodic motions is observed in this memristor-based Shinrik's circuit and the experimental results are consistent with that of the calculations through the discrete mapping method.
本文通过离散隐式映射法对基于忆阻器的 Shinriki 电路中的复杂混沌路径进行了半解析讨论。通过离散节点准确地呈现了周期为 m（m=1,2,4 和 3,6）运动的分岔树，其中系统参数发生变化。通过倍周期分岔、鞍结分岔和 Neimark 分岔得到了相应的分岔点的临界值，这可以通过特征值分析的全局观点来确定。不稳定的周期轨道与通过数值方法获得的稳定周期轨道进行比较，可以揭示收敛过程。通过吸引子的分形来分析非对称稳定周期运动的共存。此外，还通过现场可编程门阵列（FPGA）设计了硬件实验来验证分析模型。正如预期的那样，在这个基于忆阻器的 Shinriki 电路中观察到了周期运动的演化，实验结果与通过离散映射方法的计算结果一致。
