Geodesic
Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 105-114 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34-04, 34C05, 58F14, 58F21, 92D25
Keywords: stability; limit cycle; center; bifurcation 
@article{CMJ_2007_57_1_a8,
     author = {S\'aez, Eduardo and Stange, Eduardo and Sz\'ant\'o, Iv\'an},
     title = {Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four},
     journal = {Czechoslovak Mathematical Journal},
     pages = {105--114},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309952},
     zbl = {1168.92319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a8/}
}
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Sáez, Eduardo; Stange, Eduardo; Szántó, Iván. Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 105-114. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a8/