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On the torus bifurcation in averaging theory.
- Source :
-
Journal of Differential Equations . Apr2020, Vol. 268 Issue 8, p4555-4576. 22p. - Publication Year :
- 2020
-
Abstract
- In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2 D nonautonomous differential equations. Our strategy consists in looking for generic conditions on the averaged functions that ensure the existence of a curve in the parameter space characterized by a Neimark-Sacker bifurcation in the corresponding Poincaré map. A Neimark-Sacker bifurcation for planar maps consists in the birth of an invariant closed curve from a fixed point, as the fixed point changes stability. In addition, we apply our results to study a torus bifurcation in a family of 3 D vector fields. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 268
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 141636629
- Full Text :
- https://doi.org/10.1016/j.jde.2019.10.031