Nonchaotic attractor with a highly fluctuating finite-time Lyapunov exponent in a hybrid optical system

We discuss the birth of the Strange nonchaotic attractor (SNA) when the sys tem has large fluctuations of the finite-time Lyapunov exponents. We find t hat chaotic and periodic behaviors can be achieved, in turn, by a nearly si nusoidal perturbation. If the time interval of the chaotic divergence is lo ng enough and the perturbations are always added, it will be enlarged by a positive finite Lyapunov exponent. The attractor created by a perturbation can be an SNA. Also, we prove the existence of a SNA by calculating the ext ernal phase sensitivity property and the local Lyapunov exponents.