This paper investigates the emergence and control of chaos in superconducting quantum interference devices using spectral analysis and Lyapunov exponent analysis. We derive state equations based on Josephson effects, analyze dynamical features of SQUID under different parametrical regimes and find the route from period to chaos. To clarify how initial values influence system evolution, we study the evolution of the adjacent trajectories of two nearby points in phase space and introduce the Lyapunov exponent as an index. We plot the curves of the Lyapunov exponent versus different parameters to show the switch between periodic state and chaotic state, and realize the control of chaos by tuning the bias current of SQUID.
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