Bifurcation and Chaos in Josephson Circuit

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.