Transients in a time-dependent logistic map

We study the one-dimensional logistic map with parametric perturbation. Usi ng a small periodic function as the perturbation, new attractors slay appea r. Beside these new attractors, complex attractors exist and are responsibl e for transients in many trajectories. We observe that each one of these tr ansients is characterized by a power law decay. We find the exponent relate d to this decay. (C) 2001 Elsevier Science B,V. All rights reserved.