General Systems View in Ecosystem Theory and Ecosystem Modelling

Abstract

Ecosystems are described as open systems for energy, matter and information. They are characterised by nonequilibrium processes and multiple stationary states. A general system description used in state space theory, dynamical system theory and automata theory is given by non-linear and instationary multiple operators F and G where F: X × U → X with x = F(x, u) and G: X × U → Y with y = G(x, u). In this cases ecosystem models are presented by differential equations describing the changes of systems behaviour in space or time. Another concept to model ecosystems is the use of category theory. Each ecosystem and also its subsystems or components will be understood as stochastic automata (S-automata). The interpretation of an abstract automaton A as an algebraic structure S leads to an algebraic automata description and consequently to formulations by category theory. Then, an ecosystem is represented by a category which result from other categories by an inclusion functors. The goal of application of algebraic methods consists of a unified and general mathematical description of the biocoenotic structure and functioning including stochastic interrelationships within the system and with its environment.