Josephson电路中的分岔与混沌

Bifurcation and Chaos in Josephson Circuit

为了揭示电路系统丰富的非线性动力学行为,提高电路系统的稳定性,避免混沌对元器件的危害,针对一类特殊的Josephson电路,应用微分方程理论中的Lyapunov直接方法、非线性动力学方法以及改进的数值计算方法,分析了系统的稳定性、分岔与混沌,通过分岔图、最大Lyapunov指数图分析了系统参数对其稳定性的影响以及复杂的分岔结构,并进一步通过时间相应图、相图、频谱图和Poincaré映射图进一步揭示了该系统的混沌运动.研究结果表明,映射延拓综合法提高了计算精度和速度,并发现,系统在一定参数条件下存在周期泡、混沌泡和对称破缺分岔等新现象.

In order to discover abundant nonlinear dynamic behaviors, the study improves the stability of circuit systems and avoid chaos to the damage of electric component, the stability and bifurcation of Josephson circuit is analyzed by direct Lyapuonv method of ordinary equation theory. By applying bifurcation diagram, the largest Lyapunov exponent diagram are presented to analyze the stability and bifurcational structure as parameter varies. The chaotic motion of the system is studied by time series portrait,power spectrum portrait and Poincare map portrait. The results show：map and continuation comprehensive method improves accuracy and velocity, and attractor bubbles sandwiched by symmetry-breaking are observed in some condition. The study provides a new way for designing some circuit systems.