基于一阶广义忆阻器的文氏桥混沌振荡器研究∗

摘要

Through introducing a generalized memristor and an LC absorbing network into Wien-bridge oscillator, a kind of memristive Wien-bridge chaotic oscillator is proposed. The dynamical model of the memristive Wien-bridge chaotic oscillator is established, based on which the equilibrium points and their stabilities are studied and the dynamical behaviors are further analyzed when the circuit element parameters are varied. The research findings indicate that the memristive Wien-bridge chaotic oscillator has three determinative equilibrium points and their stabilities depend on the circuit element parameters, and that there exist complex nonlinear phenomena including periodic oscillations, chaotic oscillations and fast-slow effects when the parameters are changed. The experimental circuit is simple and easy to realize. The experimental waveforms and numerical simulations are consistent with each other, which well verify the theoretical analyses.%通过在文氏桥振荡器中引入广义忆阻器和LC吸收网络，提出了一种忆阻文氏桥混沌振荡器。建立了忆阻文氏桥混沌振荡器的动力学模型，研究了它的平衡点和稳定性，进一步开展了电路元件参数变化时的动力学行为分析。研究发现，忆阻文氏桥混沌振荡器有3个确定的平衡点，其稳定性取决于电路元件参数，当参数发生变化时，存在周期振荡、混沌振荡、快慢效应等复杂的非线性现象。实验电路简单易制作，实验波形和数值仿真一致，较好地验证了理论分析结果。