Use of a Fourier Decomposition Technique in Aquatic Ecosystems Modelling

Summary

A quasilinear system of ordinary first-order differential equations of the type frequently used in ecosystems modelling (including mathematical models of aquatic ecosystems) is considered. It is assumed that the system is subject to periodical changes in coefficients and/or right-hand sides (due to diurnal or seasonal character of the described ecological processes). The periodic component of the state variables caused by these disturbances is considered to be small enough to allow usage of first-order Taylor formulae. Under these assumptions a decomposition of the system dynamics into “the slow motion” component and first-order Fourier harmonics is performed. The resulting set of equations can be solved with large time steps, still preserving information on the periodic as well as the smooth average components of dynamical behavoir of the initial system. The performance of the method is evaluated using an algae growth equation, the only growth limiting factor being that of light availability. The results acquired suggest the proposed method is useful both for adjusting the average motion component and for evaluation of the diurnal dynamics of algae. Further uses of the method are discussed and proposed.