Towards Accurate PWL Approximations of Parameter-Dependent Nonlinear Dynamical Systems With Equilibria and Limit Cycles

Author

Storace, Marco ; Bizzarri, Federico

Author_Institution

Biophys. & Electron. Eng. Dept., Univ. of Genoa, Genova

Volume

54

Issue

3

fYear

2007

fDate

3/1/2007 12:00:00 AM

Firstpage

620

Lastpage

631

Abstract

This paper deals with piecewise-linear (PWL) approximations of nonlinear dynamical systems dependent on parameters and allowing the presence of few equilibria and/or limit cycles only. A method to derive the parameters of the PWL model is proposed that is based on the minimization of functionals defined to take into account a priori some dynamical features of the systems to be approximated. The method is validated by applying it to two simple dynamical systems, i.e., the cusp bifurcation normal form and the supercritical Hopf bifurcation normal form. The robustness of the approximations is checked, with a view to circuit implementations

Keywords

bifurcation; function approximation; nonlinear dynamical systems; piecewise linear techniques; PWL approximations; bifurcation analysis; cusp bifurcation normal form; equilibria; function approximation; functional minimization; limit cycles; parameter-dependent nonlinear dynamical systems; piecewise-linear approximations; supercritical Hopf bifurcation normal form; variational methods; Approximation methods; Bifurcation; Biological system modeling; Circuit synthesis; Function approximation; Limit-cycles; Minimization; Neurons; Nonlinear dynamical systems; Piecewise linear techniques; Bifurcation analysis; function approximation; nonlinear dynamical systems; piecewise-linear (PWL) approximation techniques; variational methods;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2006.887623

Filename

4126807