Existence and Characterization of Strange Nonchaotic Attractors in Nonlinear Systems

Evidence has accumulated in recent years of the occurrence, in certain nonlinear systems. of strange nonchaotic attractors. that is attractors whose geometrical character is not simple, but on and near to which the exponential divergence of trajectories. characteristic of chaotic behaviour. does not occur. This behaviour has implications for predictability; small errors in initial conditions grow much more slowly than in a chaotic system. Such attractors occur commonly in quasiperiodically forced nonlinear oscillators. where their range of existence in parameter space is substantial; we describe two particular cases, one restricted to mechanics. the other to chemistry. Long nonchaotic transients occur in other system. Xloht cvidcnce for strange nonchaotic attractors arises from numerical expcrimcnts. and certain spectral features have been proposed [F. Romciras and E. Ott, Plrys. Rev. h3S. 4414 (1YS7)] as distinguishing chsractcristics. Some analytical methods are also indicated which give plausible and, as compnrcd with numerical results. quite accurate bounds in parameter space for their existence.