Lost solution and chaos

Lost solution is an interesting phenomenon in oscillators. It implies sudden change of oscillation amplitude due to slight change of system parameters. The authors show two types of lost solution from a second order piecewise linear system. With a slight change of system parameters, the first one is rapid continuous change of periodic attractors. Chaos and related bifurcation from a periodically forced lost solution system are shown. Specifically the amplitude and DC component in the external force are taken as control parameters. As the DC component varies, a periodic response changes chaos via period doubling bifurcation and a sudden change of attractor size is confirmed. As the amplitude varies, the size of chaotic attractor grows rapidly and various periodic windows are observed. These phenomena are characterized by Lyapunov exponents which is calculated by piecewise exact solutions. Also, the chaotic response was verified by laboratory experiments