Matrix Methods and Spectral Analysis

Abstract

Environmental systems may in some cases be described on the basis of the output, or response, of the system to an input, or perturbation [1]. Even if the internal structure of the system is not understood, such input-output analysis can provide at least a partial basis for predicting the evolution of the system. For example, an ecosystem might consist of a number, N, of unique species. Each species might have some sensitivity to each of several pollutants present in the environment, meaning the species will respond to the presence ofthat pollutant (i.e. the pollutant perturbs the species, with the response being a change in the state vector describing the health of that species). If each species is exposed to the full range of pollutants simultaneously, the total response of each species is related to the composite effect of all of the pollutants acting simultaneously.