The project will focus on linking two different views of reality: the statistical view, which treats everything as a single observation independent of others; and the dynamic view, where we look at how things are connected to each other. Here, the degrees of freedom will be defined by the number of drivers of the system.
The degrees of freedom of a dynamic system are given by the number of independent drivers. Along with the evolution of a system, properties may emerge that add more degrees of freedom. In geometry the dimension of an object is defined by its extensions along a degree of freedom. A curve is 1-dimensional, an area 2-dimensional, a body 3-dimensional, and evolution over time adds a fourth dimension. The Rényi-dimensions Dq(q=0,1,2) of dynamic systems resemble a generalization of the geometric dimensions assessing additional aspects contributing to the degrees of freedom of an object or system.
The Ergodic Theory of Chaos provides two additional measures:
The goals for the project are to:
The main outcomes of the project are:
Future strategies include integration of the results into next generation vegetation models, with variable complexity, and application to other models in natural, economic, social sciences.
The FRED team consist of members from IIASA programs Ecosystems Services and Management and Advanced Systems Analysis Programs and institutions BOKU University, Towson University, University of Kwa Zulu Natal, and the Institute of Advanced Study.
Last edited: 22 September 2016
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