A proof of Perko's conjectures for the Bogdanov-Takens system
The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150601 |
| Online Access: | https://ddd.uab.cat/record/150601 https://dx.doi.org/urn:doi:10.1016/j.jde.2013.07.006 |
| Access Level: | Open access |
| Keyword: | Homoclinic connection Location of limit cycles Bifurcation of limit cycles Global description of bifurcation curve |
| Summary: | The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve. |
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