Fluctuations in Systems with Multiple Steady States. Application to Lanchester Equations.

Abstract

We consider the effects of small random perturbations on deterministic systems of differential equations. The systems of interest have a steady state that is a saddle point. A first exit problem is formulated. The quantity of basic interest is the probability of exit from a band around the deterministic separatrix through a specified boundary, conditioned on initial position. A technique for the approximate calculation of this probability is given. As an example, we show how the theory applies to the calculation of the probability of victory in a combat that has a stochastic component. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1978
Accession Number
ADA071472

Entities

People

  • Marc Mangel

Organizations

  • Center for Naval Analyses

Tags

Communities of Interest

  • Energy and Power Technologies
  • Human Systems

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Data Science
  • Differential Equations
  • Equations
  • Information Science
  • Lanchester Equations
  • Maintenance Personnel
  • Mathematics
  • Naval Air Stations
  • Naval Shore Facilities
  • Operations Research
  • Political Science
  • Probability
  • Random Variables
  • Statistics
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.