Physical Review E 63, (2001)
Abstract of the article

Stochastic multiresonance in a chaotic map with fractal basins of attraction


S. Matyja¶kiewicz 1,2 A. Krawiecki 1 J. A. Hołyst 1,2,3 K. Kacperski 3,1 and W. Ebeling 2
1 Faculty of Physics, Warsaw University of Technology Koszykowa 75, PL-00-662 Warsaw, Poland
2 Institute of Physics, Humboldt University at Berlin, Invalidenstrasse 110, D-10115 Berlin, Germany
3 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany

Noise-free stochastic resonance in a chaotic kicked spin model at the edge of the attractor merging crisis is considered. The output signal reflects the occurrence of crisis-induced jumps between the two parts of the attractor. As the control parameter-the amplitude of the magnetic field pulses-is varied, the signal-to-noise ratio shows plateaus and multiple maxima, thus stochastic multiresonance is observed. It is shown that the multiresonance occurs due to a fractal structure of the precritical attractors and their basins. In the adiabatic approximation theoretical expression for the signal-to-noise ratio is derived, based on the theory of oscillations in average crisis-induced transient lifetimes. Numerical and theoretical results agree quantitatively just above the threshold for crisis and qualitatively in a wide range of the control parameter.