非对称忆阻诱导的吸引子非对称演化与机理研究

紧磁滞回线是评测物理器件或数学模型是否为忆阻的关键依据，其对称特性也是忆阻的重要特征之一。该文提出一种有源非对称忆阻二极管桥模拟器，它通过改变二极管桥中并联二极管的数量可实现紧磁滞回线非对称度的控制。首先，验证了该非对称忆阻模拟器的指纹特征，并着重探讨了激励频率和对称度控制参数对紧磁滞回线非对称度的影响。进一步地，将该非对称忆阻模拟器耦合到Sallen-Key高通滤波器，构建了一种无感忆阻蔡氏电路；建立了相应的无量纲系统，并揭示了系统吸引子的非对称演化现象。结合平衡点稳定性分析、分岔分析和多吸引子状态初值空间分布，阐明了吸引子非对称演化的产生机理。结果表明，受非对称忆阻的影响，无感忆阻蔡氏电路的两个不稳定鞍焦点失去平衡，导致了非对称共存分岔、多稳定模态等行为的产生。最后，由硬件电路实验验证了理论分析与数值仿真的正确性。

Asymmetric Memristor-induced Attractor Asymmetric Evolution and Its Mechanism

The pinched hysteresis loop is the key basis to judge whether a physical device or a mathematical model is a memristor, and its symmetry property is also one of the important characteristics of a memristor. In this paper, an active asymmetric memristive diode-bridge emulator is proposed, whose asymmetry can be controlled by changing the number of parallel diodes in the diode-bridge. Firstly, the fingerprint of this asymmetric memristor emulator is tested, and the effects of excitation frequency and symmetry control parameter on the asymmetry of the pinched hysteresis loop are discussed. Thereafter, by coupling the asymmetric memristor into a Sallen-Key high-pass filter, an inductor-free memristive Chua’s circuit is constructed. The corresponding dimensionless system is built, upon which the asymmetric evolution feature of system attractor is uncovered. Based on the equilibrium stability analysis, bifurcation analysis and multiple attractors distribution in state initial space, the mechanism of attractor asymmetric evolution is clarified. The results demonstrated that, affected by the asymmetric memristor, two unstable saddle-foci of the inductor-free memristive Chua’s circuit are out of balance, resulting in the generations of asymmetric coexistence bifurcation and multi-stable mode. Finally, the correctness of theoretical analysis and numerical simulation are verified by hardware circuit experiment.