Characteristic Trajectories of Generalized Lanchester Equations.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1987
- Accession Number
- ADA185762
Entities
People
- John M. Wozencraft
- Paul H. Moose
Organizations
- Naval Postgraduate School