Accession Number : ADA185762

Title :   Characteristic Trajectories of Generalized Lanchester Equations.

Descriptive Note : Technical rept. 1 Oct 85-1 Jun 87,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA

Personal Author(s) : Wozencraft, John M ; Moose, Paul H

PDF Url : ADA185762

Report Date : Jun 1987

Pagination or Media Count : 62

Abstract : Generalized Lanchester-type differential equations are used to model attrition processes. This system of non-linear equations has multiple equilibrium solutions, which can be determined by a numerical technique called the Continuation Method when the problem's dimensionality is moderate. System dynamics are investigated and shown to depend critically on a domain of attraction defined by a tube which connects the non-negative equilibrium points and contains the dominant eigenvector at those points. Principles are presented and illustrated for mapping NM-dimensional systems into equivalent two-dimensional systems. This capability is especially important when aggregating subsystems have only four mapping NM-dimensional systems into equivalent two-dimensional systems. This capability i especially important when aggregating subsystems in multi-level systems modeling. It is shown that the two-dimensional Lanchester systems have only four distinct modes of behaviour, depending on the number of real positive equilibrium points that they have. A method is described and illustrated for reallocating attrition as state variables approach zero in order to guarantee their non-negativity.

Descriptors :   *ATTRITION, *LANCHESTER EQUATIONS, *TRAJECTORIES, DIFFERENTIAL EQUATIONS, DYNAMICS, EIGENVECTORS, EQUATIONS, MODELS, NONLINEAR ALGEBRAIC EQUATIONS, NUMERICAL METHODS AND PROCEDURES, SYSTEMS ANALYSIS, TWO DIMENSIONAL, MATHEMATICAL MODELS, AERIAL WARFARE

Subject Categories : Operations Research
      Military Operations, Strategy and Tactics

Distribution Statement : APPROVED FOR PUBLIC RELEASE