THE NOTION OF STABILITY IN OPEN DYNAMICAL SYSTEMS FROM AN ECOLOGICAL PERSPECTIVE

As opposed to closed systems, the state dynamics of open systems are additionally determined by independently acting external forces called "environment" in ecology. Ecosystems are open dynamical systems whose stability characteristics are commonly described in terms of resistance and resilience of system states towards the “disturbing” effects of external forces. The implicit ideas of invariance and attractivity of specific system states, however, are borrowed from the stability theory of closed dynamical systems and are therefore of limited utility for comprehensive representations of stability characteristics in open dynamical systems. Based on a generic formulation of dynamical input-output systems, it is demonstrated that the notion of adaptation of a system's responses (outputs) to its environment (inputs), when quantified by adaptational valuation functions, provides formulations which establish the desired extension of the ideas of stability known from closed systems. In essence, stability can then be viewed as a system's capacity to immediately or ultimately realize adapted responses. This capacity can conveniently be described for example with the aid of adaptational potentials of system states as described by the set of environments to which adaptation is possible. Regulatory and structural adaptation, which are the two forms of adaptation taking place without and with changes in system state, respectively, are shown to imply a natural hierarchy in adaptational processes. It is suggested that the involved levels of hierarchy be viewed to represent a mechanism for preserving adaptability in ecosystems, which in turn constitutes one of the most crucial components of ecosystem stability.