On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder

Douglas Duarte Novaes; Mike R Jeffrey; Marco Antonio Teixeira

On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder

Douglas Duarte Novaes, Mike R Jeffrey, Marco Antonio Teixeira

Department of Engineering Mathematics

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Abstract

This paper deals with discontinuous differential equations defined on the 2–dimensional cylinder. The main goal is to exhibit conditions for the existence of typical periodic solutions of such systems. An averaging method for computing sliding periodic solutions is developed, subject to convenient assumptions. We also apply the method to example problems. The main tools used are structural stability theory for discontinuous differential systems and Brouwer degree theory.

Original language	English
Article number	12
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Publication status	Published - 2014

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Engineering Mathematics Research Group

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2013_averaging~Submitted manuscript, 253 KB

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title = "On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder",

abstract = "This paper deals with discontinuous differential equations defined on the 2–dimensional cylinder. The main goal is to exhibit conditions for the existence of typical periodic solutions of such systems. An averaging method for computing sliding periodic solutions is developed, subject to convenient assumptions. We also apply the method to example problems. The main tools used are structural stability theory for discontinuous differential systems and Brouwer degree theory.",

author = "{Duarte Novaes}, Douglas and Jeffrey, {Mike R} and {Antonio Teixeira}, Marco",

year = "2014",

language = "English",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder

AU - Duarte Novaes, Douglas

AU - Jeffrey, Mike R

AU - Antonio Teixeira, Marco

PY - 2014

Y1 - 2014

N2 - This paper deals with discontinuous differential equations defined on the 2–dimensional cylinder. The main goal is to exhibit conditions for the existence of typical periodic solutions of such systems. An averaging method for computing sliding periodic solutions is developed, subject to convenient assumptions. We also apply the method to example problems. The main tools used are structural stability theory for discontinuous differential systems and Brouwer degree theory.

AB - This paper deals with discontinuous differential equations defined on the 2–dimensional cylinder. The main goal is to exhibit conditions for the existence of typical periodic solutions of such systems. An averaging method for computing sliding periodic solutions is developed, subject to convenient assumptions. We also apply the method to example problems. The main tools used are structural stability theory for discontinuous differential systems and Brouwer degree theory.

M3 - Article (Academic Journal)

SN - 0013-0915

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

M1 - 12

ER -

On sliding periodic solutions for piecewise continuous systems defined on the 2-cylinder

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