Time-delay version of the integrable discrete Lotka-Volterra system in terms of the LR transformations

To introduce time delay into integrable discrete systems, we present a time-delay version of the discrete Lotka-Volterra (dLV) system, which is a time-discretization of the famous predator-prey Lotka-Volterra system. Focusing on the LR transformations, which has been designed for solving symmetric eigenvalue problems, plays a key role in deriving the essential properties of the original dLV system. We also clarify asymptotic convergence in the resulting time-delay system and present an application for computing matrix eigenvalues and singular values.