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Structure-selection techniques applied to continuous-time nonlinear models. (English) Zbl 1098.34508
Summary: This paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data. The mathematical representation used is a nonlinear differential equation of the polynomial type. Some approaches that have been used in the context of discrete-time models are adapted and applied to continuous-time models. Two examples are included to illustrate the main ideas. Models obtained with and without structure selection are compared using topological analysis. The main differences between structure-selected models and complete structure models are: (i) the former are more parsimonious than the latter, (ii) a predefined fixed-point configuration can be guaranteed for the former, and (iii) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.

MSC:
34A34 Nonlinear ordinary differential equations and systems
26C05 Real polynomials: analytic properties, etc.
37M10 Time series analysis of dynamical systems
37N99 Applications of dynamical systems
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