Strange nonchaotic attractors in the quasiperiodically forced logistic map

Abstract

Different mechanisms for the creation of strange nonchaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterized through the behavior of the largest nontrivial Lyapunov exponent, as well as through the characteristic distributions of finite-time Lyapunov exponents. Strange nonchaotic attractors can be created at a saddle-node bifurcation when the dynamics shows type-I intermittency; this intermittent transition, which is studied in detail, is characterized through scaling exponents. Band-merging crises through which dynamics remains nonchaotic are also studied, and correspondence is made with analogous behavior in the unforced logistic map. Robustness of these phenomena with respect to additive noise is investigated.