Exact solutions to chaotic and stochastic systems

Details Exact solutions to chaotic and stochastic systems Exact solutions to chaotic and stochastic systems

2001-01-26

arxiv.org/abs/nlin/0101049v2

Chaos 11, 1 (2001)

Nonlinear Sciences

Chaotic Dynamics

31 pages, 18 figures (.eps). To appear in Chaos, March 2001

Scientific paper

10.1063/1.1350455

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time-series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

Affiliated with

Also associated with

No associations

Rating

Exact solutions to chaotic and stochastic systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exact solutions to chaotic and stochastic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact solutions to chaotic and stochastic systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-390082