Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example

Marco BERGAMI; Federico BIZZARRI; Andrea CARLEVARO; Marco STORACE

doi:10.1093/ietfec/e89-a.10.2759

Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example

Marco BERGAMI, Federico BIZZARRI, Andrea CARLEVARO, Marco STORACE

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In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.10 pp.2759-2766

Publication Date: 2006/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.10.2759

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

Category: Oscillation, Dynamics and Chaos

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Marco BERGAMI, Federico BIZZARRI, Andrea CARLEVARO, Marco STORACE, "Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 10, pp. 2759-2766, October 2006, doi: 10.1093/ietfec/e89-a.10.2759.
Abstract: In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.10.2759/_p

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@ARTICLE{e89-a_10_2759,
author={Marco BERGAMI, Federico BIZZARRI, Andrea CARLEVARO, Marco STORACE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example},
year={2006},
volume={E89-A},
number={10},
pages={2759-2766},
abstract={In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.},
keywords={},
doi={10.1093/ietfec/e89-a.10.2759},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Structurally Stable PWL Approximation of Nonlinear Dynamical Systems Admitting Limit Cycles: An Example
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2759
EP - 2766
AU - Marco BERGAMI
AU - Federico BIZZARRI
AU - Andrea CARLEVARO
AU - Marco STORACE
PY - 2006
DO - 10.1093/ietfec/e89-a.10.2759
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2006
AB - In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.
ER -