Predicting periodic solutions of cyclic Lotka-Volterra equations with dynamic mode decomposition

Abstract

Cyclic Lotka-Volterra systems in form of ODEs and PDEs are solved by linearly implicit Kahan's method, that preserves the quadratic Poisson bracket, phase space volume, Hamiltonian ad Casimirs. The solutions are predicted applying dynamic mode decomposition (DMD). Numerical results show that the extended DMD with quadratic dictionaries and Hankel DMD with the delay embeddings, predict the periodic solutions with high accuracy, whereas the standard DMD fails. The Hamiltonians and Casimirs are also preserved accurately by the extend DMD and Hankel DMD.