Noise Induced Switching in Delayed Systems

Abstract

We consider the problem of switching in stochastic systems with delayed feedback. A general variational formation is derived for the switch rate in a stochastic differential delay equation where the noise sources is of general form. The resulting equations of motion and boundary conditions describe the optimal escape path which maximizes the probability of escape. Analyzing the dynamics along the optimal path yields exponents of the distribution in terms of delay time, dissipation, and noise intensity. Theoretical predictions compare very well with numerical simulations in both additive and multiplicative noise cases, even outside of regions where the delay is assumed to be small.

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Document Details

Document Type
Technical Report
Publication Date
Apr 27, 2012
Accession Number
ADA561020

Entities

People

  • Ira B. Schwartz
  • Lora Billings
  • Mark Dykman
  • Thomas W. Carr

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Boundaries
  • Differential Equations
  • Dissipation
  • Dynamics
  • Equations
  • Equations Of Motion
  • Feedback
  • Gaussian Noise
  • Intensity
  • Mathematics
  • Military Research
  • Physics
  • Probability
  • Simulations
  • Steady State
  • Switching

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Calculus or Mathematical Analysis
  • Control Systems Engineering.