On Qualitative Lanchestrian Models of Combat Incorporating Logistics.
Abstract
We initiate the study of a family of models of military combat which include classical linear Lanchestrian models as a special case. These models introduce the additional concept of one or several columns providing supplies to one of the forces. It is assumed that the other force is defending an already supplied position or is prepared only for a short campaign. The models are designed so as to have solutions that are primarily qualitative in character. They have the form of a linear system of differential equations du/dt = Au + F(t) where u is a vector with m > or = 3 components, A is an m x m constant matrix and F is a given time dependent vector with m components. The differential equations are to be solved subject to certain stopping rules. When we say that the solutions are qualitative in character, we mean that the mathematical form of the solution does not depend upon the magnitudes of the elements of the matrix A but only upon the signs of these elements. We introduce the concepts of upper and lower solutions which serve as bounds for all positive solutions of the problem. We obtain detailed results on the eigenvalues and eigenvectors of A and explicit representations of the upper and lower solutions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1979
- Accession Number
- ADA069336
Entities
People
- John S. Maybee
Organizations
- University of Colorado Boulder