Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four

Eduardo Sáez; Eduardo Stange; Iván Szántó

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 105-114
  • ISSN: 0011-4642

Abstract

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A class of degree four differential systems that have an invariant conic x 2 + C y 2 = 1 , C ∈ ℝ , is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.

How to cite

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Sáez, Eduardo, Stange, Eduardo, and Szántó, Iván. "Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four." Czechoslovak Mathematical Journal 57.1 (2007): 105-114. <http://eudml.org/doc/31116>.

@article{Sáez2007,
abstract = {A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in \{\mathbb \{R\}\}$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.},
author = {Sáez, Eduardo, Stange, Eduardo, Szántó, Iván},
journal = {Czechoslovak Mathematical Journal},
keywords = {stability; limit cycle; center; bifurcation; stability; limit cycles; center; bifurcations},
language = {eng},
number = {1},
pages = {105-114},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four},
url = {http://eudml.org/doc/31116},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Sáez, Eduardo
AU - Stange, Eduardo
AU - Szántó, Iván
TI - Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 105
EP - 114
AB - A class of degree four differential systems that have an invariant conic $ x^2+Cy^2=1$, $C\in {\mathbb {R}}$, is examined. We show the coexistence of small amplitude limit cycles, large amplitude limit cycles, and invariant algebraic curves under perturbations of the coefficients of the systems.
LA - eng
KW - stability; limit cycle; center; bifurcation; stability; limit cycles; center; bifurcations
UR - http://eudml.org/doc/31116
ER -

References

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