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Dynamical Systems

Patrick McGivern

Pages 193 - 195

The term dynamical system is used in a loose sense and in a precise sense which is associated with dynamical systems theory. Any object or group of objects subject to a development in time can loosely be called a dynamical system; in this sense dynamical systems are closely associated with processes. For the more precise meaning of the term one has to distinguish – as in all cases of mathematical modeling – between (i) the (concrete) system being modeled and (ii) the (abstract) mathematical structure used to model that concrete system. Either system can be referred to as a dynamical system. A dynamical system in sense (ii) is represented by its states at given times and a rule that evolves the states to states at other times. More technically, a dynamical system (in sense (ii)) is a structure <M, ft, T>, where M is the multidimensional state or phase space of the system, ft is the evolution rule that relates the state at each time to states at other times, and T is the onedimensional space of points in time (so that t ∈ T).

1Department of Philosophy, University of Wollongong

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