Universal mechanism for the intermittent route to strange nonchaotic attractors in quasiperiodically forced systems

Abstract

To examine the universality for the intermittent route to strange nonchaotic attractors (SNAs), we investigate the quasiperiodically forced Henon map, ring map and Toda oscillator which are high-dimensional invertible systems. In these invertible systems, dynamical transition to an intermittent SNA occurs via a phase-dependent saddle–node bifurcation, when a smooth torus collides with a 'ring-shaped' unstable set. We note that this bifurcation mechanism for the appearance of intermittent SNAs is the same as that found in a simple system of the quasiperiodically forced noninvertible logistic map. Hence, the intermittent route to SNAs seems to be 'universal', in the sense that it occurs through the same mechanism in typical quasiperiodically forced systems of different nature.