Positive Lyapunov exponents calculated from time series of strange nonchaotic-attractors - art. no. 026220

Time-series methods for estimating Lyapunov exponents may give a positive e xponent when they are applied to the time series of strange nonchaotic syst ems. Strange nonchaotic systems are characterized by expanding and contract ing regions in phase space that result in repeatedly expanding or contracti ng trajectories. Using time-series methods, the maximum time-series Lyapuno v exponent is calculated as an average of the locally most expanding expone nts that characterize the divergence of nearby trajectories following a rec onstructed attractor over time. A positive exponent is reported by time-ser ies methods for trajectories in an expanding region. While in a converging region, the most expanding dynamics are related to the quasiperiodic drivin g force. Statistically, a zero exponent related to the quasiperiodic force is obtained through time-series methods within converging regions. As a res ult, the calculated maximum Lyapunov exponent is positive.