The notion of stability in mathematics, biology, ecology and environmental sustainability

Abstract: The term “stability ” has many different meanings and its interpretation and application in various sciences is not absolutely identical. Historically, stability has been first formally defined in mathematical form by Lyapunov to describe equilibrium behaviour of the solar system. Lyapunov stability considers the behaviour of a system solution if its initial state is in the neighbourhood of an equilibrium point. Conceptually, it states that the equilibrium point is stable if all solutions originating in its neighbourhood forever remain “close enough ” to equilibrium. Due to its precise definition and well-established mathematical technique, Lyapunov stability has found a widespread application outside its original context, particularly to analyse solutions of mathematical models of biological communities in order to determine conditions they must satisfy to be stable. Research of this kind has been a dominating trend and, in words of Justus (2006), set much of the agenda of twentieth century mathematical ecology. There are, however, intrinsic features of the ecological systems that distinguish them from physical systems and limit a mechanical application of mathematical technique of stability study. An ecosystem is comprised of living (biotic) components and their non-living (abiotic) factors. A biotic part of an ecosystem (i.e., plants, animals and micro-organisms) is organized in hierarchical structures according to their role in the energetic and metabolic processes called trophic levels