Biophysical and Electronic Engineering Department, University of GenoaVia Opera Pia 11a, I-16145 Genova, ItalyEmail: Marco.Storace@unige.itAbstract—This paper concerns the piecewise-linear (PWL) approximation of the cusp normal form,which is a well-known nonlinear dynamical system.Evenifappliedtoasimpleexample,themethodcanbeeasily generalized and allows one to define a strategyto calculate the optimal coefficients for the PWL ap-proximation. It is possible to choose either an approx-imation accuracy almost uniform all over the approx-imation domain, or an approximation particularly ac-curateintheneighborhoodsofsignificantsetsofpoints(bifurcation curves or invariant sets), or a compromisebetween these two situations. The numerical results inthe considered example confirm the reliability of theproposed approach.1. IntroductionThis paper deals with the piecewise-linear (PWL)approximation (in view of structurally stable circuitimplementations) [1] of known nonlinear dynamicalsystems with bounded dynamics governed by the fol-lowing set of ordinary differential equations:
[1]
Y. Kuznetsov.
Elements of Applied Bifurcation Theory
,
2023,
Applied Mathematical Sciences.
[2]
Marco Storace,et al.
Piecewise-linear approximation of nonlinear dynamical systems
,
2004,
IEEE Transactions on Circuits and Systems I: Regular Papers.
[3]
Alfredo C. Desages,et al.
Orthonormal high-level canonical PWL functions with applications to model reduction
,
2000
.
[4]
Miss A.O. Penney.
(b)
,
1974,
The New Yale Book of Quotations.
[5]
Marco Storace,et al.
A method for the approximate synthesis of cellular non‐linear networks—Part 1: Circuit definition
,
2003,
Int. J. Circuit Theory Appl..
[6]
Marco Storace,et al.
Towards analog implementations of PWL two‐dimensional non‐linear functions
,
2005,
Int. J. Circuit Theory Appl..
[7]
Pedro Julián,et al.
Synthesis of multiport resistors with piecewise-linear characteristics: a mixed-signal architecture
,
2005,
Int. J. Circuit Theory Appl..