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. The ecosystem processes (like production, destruction, respiration, transformation, etc.) as well as intro- and interspecific interactions (e.g., competition, predation, parasitism, mutualisms, and so on) are characterized by the quantitative values of the corresponding parameters. An adequate description of an ecosystem (E) is a three-compartment tuple, which includes a set {C} of biotic components and abiotic factors (i.e., ecosystem constituents), a set {S} of their particular assemblages and interrelationships (i.e., ecosystem structure) and a set {P} of ecosystem parameters designating quantitative values of the ecological processes involving components, factors and interactions between them. Intuitively, ecosystem stability is understood as an ability to persist in the course of a sufficiently long time in spite of exogenous perturbations. But, unlike systems studied in physics, parameter values and system structure of an ecosystem are not fixed, and exogenous perturbations may affect and change different aspects of the real-world ecosystem, including: (1) initial conditions (C-stress); (2) environmental abiotic factors (A-stress); (3) biological populations in biotic assemblages (B-stress); (3) parameter values (P-stress); and (4) ecosystem structure (S-stress). An ecosystem affected by S-type of stress can cross a critical point and shift to a new structural quality. From this perspective, the perturbed dynamics of an ecosystem is a sequence of critical time instants, at which structural transformations occur. An ecosystem passing over a critical point must be modelled as a new system, though a new model can, to a different extent, inherit certain features of the old one (Pusachenko, 1989). Consequently, ecological stability can be studied only within a structural domain, and a new model has to be built and analysed once the ecosystem has crossed a critical point. Any judgement about ecosystem stability or instability is also valid only for a given structural domain. Groups of dominant species, primary plant-based functions of productivity / respiration / decomposition as well as nutrient cycling and energy transfer / loss can be used as indicators of critical transitions leading the ecosystem to a new structural domain.
