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Bifurcation theory of limit cycles by higher order Melnikov functions and applications.
- Source :
-
Journal of Differential Equations . Sep2024, Vol. 403, p29-66. 38p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study Poincaré, Hopf and homoclinic bifurcations of limit cycles for planar near-Hamiltonian systems. Our main results establish Hopf and homoclinic bifurcation theories by higher order Melnikov functions, obtaining conditions on upper bounds and lower bounds of the maximum number of limit cycles. As an application, we concern a cubic near-Hamiltonian system, and study Hopf and homoclinic bifurcations in detail, finding more limit cycles than [26]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIMIT cycles
*BIFURCATION theory
*HOPF bifurcations
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 403
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 177750262
- Full Text :
- https://doi.org/10.1016/j.jde.2024.04.036