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Triangulation, Modelling and Controlling Dynamical Systems
Theory and Applications
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Chaos attracted attention of scientists for centuries§but not until §recently we started to understand it. We encounter§chaotic systems in §our everyday lives, from washing machines to the§stock market. They §seem to be random but in fact they are dynamical§systems very §sensitive to changes. This book describes a§triangulation method to §study and to model dynamical systems derived from§observed data. §The idea of the triangulation method is to construct§a 'net' of §simplices, geometrical objects like triangles andtetrahedra that §connect data points. This natural grid is then used§to approximate an §unknown system by a piecewise linear interpolation.§Within this §simplicial framework it is shown how to find a fixed§point of the §interpolated system. Examples with a computer§software illustrate how §to reconstruct control a dynamical system in a§neighbourhood of its §fixed point.
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