Accession Number:

ADA357013

Title:

The Effects of Noise on Nonlinear Systems Near Crisis

Descriptive Note:

Final rept.

Corporate Author:

MARYLAND UNIV COLLEGE PARK

Personal Author(s):

Report Date:

1991-01-01

Pagination or Media Count:

82.0

Abstract:

We consider the influence of random noise on low-dimensional, nonlinear dynamical systems with parameters near values leading to a crisis in the absence of noise. In a crisis, one of several characteristic changes in a chaotic attractor takes place as a system parameter p passes through its crisis value Pc. For each type of change, there is a characteristic temporal behavior of orbits after the crisis pPc by convention, with a characteristic time scale t. For an important class of deterministic systems, the dependence of t on p is tp-Pc-gamma for p slightly greater than Pc. When noise is added to a system with pPc, orbits can exhibit the same sorts of characteristic temporal behavior as in the deterministic case for pPc a noise-induced crisis. Our main result is that for systems whose characteristic times scale as above in the zero-noise limit, the characteristic time in the noisy case scales as tsigma-gamma gPc - psigma, where sigma is the characteristic strength of the noise, g. is a non-universal function depending on the system and noise, and gamma is the critical exponent of the corresponding deterministic crisis. Illustrative numerical examples are given for two-dimensional maps and a three-dimensional flow. In addition, the relevance of the noise scaling law to experimental situations is discussed.

Subject Categories:

  • Operations Research
  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE