Can Strange Nonchaotic Dynamics be induced through Stochastic Driving?

Details Can Strange Nonchaotic Dynamics be induced through Stochastic Driving? Can Strange Nonchaotic Dynamics be induced through Stochastic Driving?

1999-10-29

arxiv.org/abs/chao-dyn/9911002v1

Nonlinear Sciences

Chaotic Dynamics

4 Pages, 3 Figures

Scientific paper

Upon addition of noise, chaotic motion in low-dimensional dynamical systems can sometimes be transformed into nonchaotic dynamics: namely, the largest Lyapunov exponent can be made nonpositive. We study this phenomenon in model systems with a view to understanding the circumstances when such behaviour is possible. This technique for inducing ``order'' through stochastic driving works by modifying the invariant measure on the attractor: by appropriately increasing measure on those portions of the attractor where the dynamics is contracting, the overall dynamics can be made nonchaotic, however {\it not} a strange nonchaotic attractor. Alternately, by decreasing measure on contracting regions, the largest Lyapunov exponent can be enhanced. A number of different chaos control and anticontrol techniques are known to function on this paradigm.

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