Moment instabilities in multidimensional systems with noise

Details Moment instabilities in multidimensional systems with noise Moment instabilities in multidimensional systems with noise

2004-04-14

arxiv.org/abs/math-ph/0404035v2

Eur. Phys. J. B, 43 (2), p. 221, 2005

Physics

Mathematical Physics

21 pages, 15 figures

Scientific paper

10.1140/epjb/e2005-00045-3

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a simple, dominant eigenvalue and stationary, white noise. When the noise is small, we obtain general expressions for the approximate asymptotic distribution and moment Lyapunov exponents. In the case of larger noise, the second moment is calculated using a different approach, which gives an exact result for some types of noise. We analyze the dependence of the moments on the system's dimension, relevant system properties, the form of the noise, and the magnitude of the noise. We determine a critical value for noise strength, as a function of the unperturbed system's convergence rate, above which the second moment diverges and large fluctuations are likely. Analytical results are validated by numerical simulations. We show that our results cannot be extended to the continuous time limit except in certain special cases.

Affiliated with

Also associated with

No associations

Rating

Moment instabilities in multidimensional systems with noise 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 Moment instabilities in multidimensional systems with noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moment instabilities in multidimensional systems with noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-556782