Structure selection for global vector field reconstruction by using the identification of fixed points

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Abstract
Global vector field reconstruction is a well established technique to provide phenomenological models from nonlinear data, in particular when all information is contained in a so-called standard function. In the case when the standard function is taken as a ratio of polynomials, we establish that information about the fixed points of the system can be automatically retrieved from the data, allowing one to build a better model by selecting an appropriate structure. The method is exemplified in the case of the variable z of the Rössler system, which constitutes a rather acid test case.

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