Influence of fractal structures on chaotic crises and stochastic resonance

We present analytical and numerical studies of a chaotic model of a kicked magnetic moment (spin) in the presence of anisotropy and damping. There is an influence of the fractal structure of attractors and basins of attraction on mean transient lifetimes near chaotic crises and on noise-free stochastic resonance in this system. The observed oscillations of average transient times emerging on the background of the well-known power scaling law can be explained by simple geometric models of overlapping fractal sets. Using as the control parameter the amplitude of magnetic field pulses one finds that such measures of stochastic resonance as the input-output correlation function or the signal-to-noise ratio show multiple maxima characteristic of stochastic multiresonance. A simple adiabatic theory which takes into account the fractal structures of this model well explains numerical simulations.