Fractal structures and noisefree stochastic multiresonance

Andrzej Krawiecki, Sławomir Matyjaśkiewicz, Krzysztof Kacperski and Janusz Hołyst

We present analytical and numerical report on the studies of the phenomenon of noisefree stochastic multiresonance that appers in a natural way in system where the threshold crossing probability has a nonmonotonous derivative with respect to the control parameter. In particular, we consider periodically driven Henon map and periodically driven 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 probability of jump near chaotic crises and on noisefree stochastic resonance in this systems. The observed oscillations of average probability of jump emerging on the background of the well-known power scaling law can be explained by simple geometric models of overlapping fractal sets. The spectral power amplification as a function of the control parameter can be easily obtained from the postcr itical average probability of chaotic jumps.