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 attractio n on mean transient lifetimes near chaotic crises and on noise-free stochas tic resonance in this system. The observed oscillations of average transien t 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 t hat such measures of stochastic resonance as the input-output correlation f unction or the signal-to-noise ratio show multiple maxima characteristic of stochastic multiresonance. A simple adiabatic theory which takes into acco unt the fractal structures of this model well explains numerical simulation s.