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math.DS2013
Bifurcation diagram and stability for a one-parameter family of planar vector fields
Johanna D. García-Saldaña, Armengol Gasull, Hector Giacomini
We consider the 1-parameter family of planar quintic systems, , , introduced by A. Bacciotti in 1985. It is known that it has at most one limit cy…
math.DS2013★ 1 cited
A proof of Perko's conjectures for the Bogdanov-Takens system
Armengol Gasull, Hector Giacomini, Set Perez-Gonzalez +1
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…