A numerical factorization of characteristic polynomial by the discrete hungry Lotka-Volterra system(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

Abstract

The discrete hungry Lotka-Volterra (dhLV) system is a generalization of the discrete Lotka-Volterra (dLV) system which stands for a prey-predator model in mathematical biology. In this paper, we show an existence of some invariants, which are independent of the discrete time n, expressed by dhLV variables and the asymptotic behavior of dhLV variables as n→∞, Some characteristic polynomials are then factorized with the help of dhLV system. We design an algorithm for computing complex eigenvalues of a certain band matrix.