Stability Concepts in Mathematics and Ecology and Their Application to Social Systems

摘要

A review of stability concepts is presented in the context of ecological, economic, and social systems involved in a program of regional land management. A number of definitions relating to stability are provided. Other mathematical definitions include fundamental solutions, scalar functions, and temporal and absolute stability. Stability results are discussed with respect to nine theorems under the general heading of mathematical stability results together with four Lyapunov-stability theorems. Ecological arguments are considered as to complexity of the stability concept as it exists in ecology and the characteristics of simple models of ecosystems. Carefully and consistently defined stability concepts appear to have no counterparts in ecological systems. Instead, ecological systems seem to operate within a vaguely defined resilience. Such a structure in social systems probably would be more versatile and acceptable but less efficient than a stable one.