Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application

Hideaki OKAZAKI; Katsuhide FUJITA; Hirohiko HONDA; Hideo NAKANO

doi:10.1093/ietfec/e88-a.4.810

Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application

Hideaki OKAZAKI, Katsuhide FUJITA, Hirohiko HONDA, Hideo NAKANO

Full Text Views

0

Share
Cite this

Summary :

This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.4 pp.810-817

Publication Date: 2005/04/01

Publicized

Online ISSN

DOI: 10.1093/ietfec/e88-a.4.810

Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa)

Category

Cite this

Copy

Hideaki OKAZAKI, Katsuhide FUJITA, Hirohiko HONDA, Hideo NAKANO, "Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 4, pp. 810-817, April 2005, doi: 10.1093/ietfec/e88-a.4.810.
Abstract: This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.4.810/_p

Copy

@ARTICLE{e88-a_4_810,
author={Hideaki OKAZAKI, Katsuhide FUJITA, Hirohiko HONDA, Hideo NAKANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application},
year={2005},
volume={E88-A},
number={4},
pages={810-817},
abstract={This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.},
keywords={},
doi={10.1093/ietfec/e88-a.4.810},
ISSN={},
month={April},}

Copy

TY - JOUR
TI - Rigorous Verification of Poincare Map Generated by a Continuous Piece-Wise Linear Vector Field and Its Application
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 810
EP - 817
AU - Hideaki OKAZAKI
AU - Katsuhide FUJITA
AU - Hirohiko HONDA
AU - Hideo NAKANO
PY - 2005
DO - 10.1093/ietfec/e88-a.4.810
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2005
AB - This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.
ER -