Permanence and viability

Abstract

The history of Systems Analysis and its forerunners displays an interesting tension between dynamic and static viewpoints. In intention, the dynamical aspects were stressed again and again. In effect, the outcome was most often a static analysis of equilibria. One reason for this shortcoming lies obviously in the mathematical intricacies of non-equilibrium situations, which for a long time led to their neglect. Even if Poincard and other classical authors stressed the amazing complexitv of some mechanical problems, the general trend, as reflected in many a textbook, ignored such'subtleties'and concentrated on a handful of tractable equations and on localized stability analysis. It is only in the last decade that the prevalent and exciting nature of complicated asymptotic behaviour became generally recognized. This shift in perspective is due to the development of new mathematical techniques, to the spread of computing facilities and, possibly, to the growing recognition of the limits of human abilities of handle, predict or control complex situations. Other reasons for the dominating influence of equilibrium concepts in the history of Systems Analysis are of a non-mathematical nature. In the most diverse fields of physics and chemistry, ecology and economy, steady states were recognized, or at least postulated, as prime objects of study. It may be the fact that we are living today in a less stable world which has caused a shift in the focus of our interests, from being to becoming, to quote Prigogine's expression. Irreversibility, oscillations, synergetic phenomena. phase transitions, turbulence and chaos forced themselves in to the foreground of scientific investigation. Climacting ecosystems a la Clements or economic optima sensu Pareto appear in many instances now as too good to be true. The tremendous progress of equilibrium theories and optimization techniques forced the subject to level off, like a plane reaching thinner layers of the atmosphere. By their very precision, mathematical investigations restricted the domains where we are prepared to expect stable equilibria. Their existence is something which has to be proved and cannot be taken for granted. The growing interest in nonequilibrium situations has led to the emergence of new notions whose meanings have not settled down yet to formal definitions, but which, partly because of this, prove to be highly stimulating. As an example, we mention here'resilience'. a concept introduced by Holling [5] in ecological context. Loosely speaking, it measures the ability of a system to maintain its structure in the face of disturbance, but stands in contrast to the concept of stability in the strict static sense. Stability... emphasizes on equilibrium condition, low