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

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