Effect of noise on critical behavior
of different universality classes
at the chaos threshold

In studies of transitions to chaos in the context of physical systems a question of effect of an inevitable noise is of principal significance as the noise destroys subtle details of fractal structures in state space and in parameter space, formation of which is just the essence of the transition.

The idea of application of the renormalization group nethod for analysis of the effect of noise at the chaos threshold was suggested first in two articles published in the same issue of Physical Review Letters in 1981. (J.P.Crutchfield, M.Nauenberg, and J.Rudnik, and B.Shraiman, C.E.Wayne, and P.C.Martin). Both of them relate to the problem of the period doubling transition to chaos in discrete-time models (iterative maps). The authors introduced a new universal constant, which indicates how many times less should one select the noise intensity to observe one more level of the fractal-like structure associated with the period-doubling transition at the onset of chaos. Afterwards analogous approaches were elaborated by many authors for some other types of behavior at the onset of chaos or strange nonchaotic attractor.

The present section of our web-site contains results of the renormalization group analysis and illustrations of scaling properties associated with effect of noise for several types of criticality. It has been prepared in a course of work supported by joint project of DFG and RFBR(Grant No 04-02-04011).


Saratov group
of theoretical nonlinear
dynamics
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