Simple examples of one-parameter planar bifurcations.

Armengol Gasull; Rafel Prohens

Extracta Mathematicae (2000)

  • Volume: 15, Issue: 1, page 219-229
  • ISSN: 0213-8743

Abstract

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In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.

How to cite

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Gasull, Armengol, and Prohens, Rafel. "Simple examples of one-parameter planar bifurcations.." Extracta Mathematicae 15.1 (2000): 219-229. <http://eudml.org/doc/38627>.

@article{Gasull2000,
abstract = {In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.},
author = {Gasull, Armengol, Prohens, Rafel},
journal = {Extracta Mathematicae},
keywords = {Sistemas dinámicos; Bifurcación paramétrica; Ecuaciones diferenciales; Sistemas bidimensionales; one-parameter bifurcations; plane vector fields},
language = {eng},
number = {1},
pages = {219-229},
title = {Simple examples of one-parameter planar bifurcations.},
url = {http://eudml.org/doc/38627},
volume = {15},
year = {2000},
}

TY - JOUR
AU - Gasull, Armengol
AU - Prohens, Rafel
TI - Simple examples of one-parameter planar bifurcations.
JO - Extracta Mathematicae
PY - 2000
VL - 15
IS - 1
SP - 219
EP - 229
AB - In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.
LA - eng
KW - Sistemas dinámicos; Bifurcación paramétrica; Ecuaciones diferenciales; Sistemas bidimensionales; one-parameter bifurcations; plane vector fields
UR - http://eudml.org/doc/38627
ER -

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