Multipeaked probability distributions of recurrence times.
We determine probabilities of recurrence time into finite-sized, physically meaningful subsets of phase space. We consider three different autonomous chaotic systems: (i) scattering in a three-peaked potential, (ii) connected billiards, and (iii) Lorenz equations. We find multipeaked probability distributions, similar to the distributions found in (driven) stochastically resonant systems. In nondriven systems, such as ours, only monotonic decaying distributions (exponentials, stretched exponentials, power laws, and slight variations or combinations of these) have hitherto been reported. Discrete peaks in autonomous systems have as yet escaped attention in autonomous systems and correspond to specific trajectory subsets involving an integer number of loops.
Grete
Patrick
P
Max-Planck-Institut für molekulare Physiologie, Postfach 500247, 44202 Dortmund, Germany.
Markus
Mario
M