Bifurcation to strange nonchaotic attractors

Abstract

Strange nonchaotic attractors are attractors that are geometrically strange, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quasi-periodically driven dissipative dynamical systems. We investigate a route to strange nonchaotic attractors in systems with a symmetric invariant subspace. Assuming there is a quasiperiodic torus in the invariant subspace, we show that the loss of the transverse stability of the torus can lead to the birth of a strange nonchaotic attractor. A physical phenomenon accompanying this route to strange nonchaotic attractors is an extreme type of intermittency. We expect this route to be physically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic behavior is also studied.