线性延时反馈Josephson结的Hopf分岔和混沌化

摘要

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌.%In this paper, a resistive-capacitive-shunted Josephson junction with linear delayed feedback is considered. The stability of trivial solution of the controlled system is analyzed using nonlinear dynamics theory, and the theoretical results show that the stable trivial solution of the system will lose its stability via Hopf bifurcation as control parameter varies. The critical parameter condition of Hopf bifurcation is also derived. Numerical analysis of the controlled system is carried out under different parameter conditions, and the results show that the stable periodic solution generated by supercritical Hopf bifurcation may transit to chaos gradually through a process of symmetry-breaking bifurcation and period-doubling bifurcation.