Qualitative Principles of Ecology and Their Implications in Quantitative Engineering Systems

In this paper, we briefly review some fundamental qualitative features of ecological sign stability and transform these principles of ecology to a set of mathematical results in matrix theory with quantitative information, which is usually encountered in engineering sciences. This type of cross fertilization of ideas of life sciences and engineering sciences is deemed to be highly beneficial to both fields. In particular, we show in this paper what effect the signs of elements of a matrix have on the matrix properties such as eigenvalues and condition number. Similarly, it is also shown that under some assumptions on the magnitudes of the elements, predator-prey phenomenon in ecology renders some special properties like ‘normality’ to matrices. It is also shown that these predator-prey models have better robustness properties when compared to other matrices. The results presented in this paper can assist in the use of ecological system principles to build highly robust engineering systems.