Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · chao-dyn/9305009

Large Fluctuations in Stochastically Perturbed Nonlinear Systems: Applications in Computing

Robert S. Maier
View original source ↗Read source document ↗Export metadata ↓

Abstract

This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic models arising in computer science are analysed. One is a stochastic model of a communications network, resembling an Ethernet, which experiences traffic fluctuations. The other is a simple model of two dynamic data structures in the same memory space. In both models `large fluctuations' are unlikely, undesirable events. The mean time between occurrences of such events is estimated.

Explore related subjects

chao-dynnlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Robert S. Maier. 1993-05-28. Large Fluctuations in Stochastically Perturbed Nonlinear Systems: Applications in Computing. https://arxiv.org/abs/chao-dyn/9305009

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2015

The Bogdanov Map: Bifurcations, Mode Locking, and Chaos in a Dissipative System

We investigate the bifurcations and basins of attraction in the Bogdanov map, a planar quadratic map which is conjugate to the Hénon area-preserving map in its conservative limit. It undergoes a Hopf bifurcation as dissipation is added, and exhibits the panoply of mode locking, Arnold tongues, and chaos as an invariant circle grows out, finally to be destroyed in the homoclinic tangency of the manifolds of a remote saddle point. The Bogdanov map is the Euler map of a two-dimensional system of ordinary differential equations first considered by Bogdanov and Arnold in their study of the versal unfolding of the double-zero-eigenvalue singularity, and equivalently of a vector field invariant under rotation of the plane by an angle $2π$. It is a useful system in which to observe the effect of dissipative perturbations on Hamiltonian structure. In addition, we argue that the Bogdanov map provides a good approximation to the dynamics of the Poincaré maps of periodically forced oscillators.

chao-dyn↗
arXiv2012

Passive Scalars and Three-Dimensional Liouvillian Maps

Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrable cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.

chao-dyn↗