Bimodal piecewise linear dynamical systems: reduced forms. (English) Zbl 1202.34025

Summary: Piecewise linear systems constitute a class of nonlinear systems which have recently attracted the interest of researchers because of their interesting properties and the wide range of applications from which they arise. Different authors have used reduced forms when studying these systems, mostly in the case where they are observable. In this work, we focus on bimodal continuous dynamical systems (those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane) depending on two or three state variables, which are the most common piecewise linear systems found in practice. Reduced forms are obtained for general systems, not necessarily observable. As an application, we calculate the dimension of the equivalence classes.


34A36 Discontinuous ordinary differential equations
34C41 Equivalence and asymptotic equivalence of ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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