Nonlinear Dynamical Systems: Worked Examples, Perspectives and Open Problems

A first and important step in tbe construction of a mathematical model of a (biologieal) system consists of the choice of astate space. Tbe mathematical state should be a convenient representation of those physiological, chemical, physical and other relevant properties which in our conception of (or hypotheses about) reality uniquely determine the future, in the sense that for a given time course of experimental or environmental conditions (the input) we obtain a unique time course of the quantities we are interested in (the output). In seetion III.2 we made some remarks about the choice of astate space and about the construction of astate space from input-output data. Moreover, we presented a precise mathematical reformulation of the intuitive definition of "state" above in terms of a family of operators with a sentigroup property.