# Simple examples of one-parameter planar bifurcations.

Armengol Gasull; Rafel Prohens

Extracta Mathematicae (2000)

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

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topGasull, 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 -