On the convergence of a solution of the discrete Lotka-Volterra system

For arbitrary positive discrete step size 8 a determinantal solution of the discrete-time Lotka-Volterra (dLV) system is shown to asymptotically converge to the square of some singular value of a given bidiagonal matrix, where the initial value of the dLV system is uniquely determined by the entries of the matrix. Some basic properties of the solution are proved which are important for designing a new numerical algorithm for computing all of the singular values. They are a positivity of solution, a dependence of the correct initial value on delta, a sorting property and an acceleration of convergence speed by enlarging delta.