TY - JOUR
T1 - A proof of Perko's conjectures for the Bogdanov-Takens system
AU - Gasull, A.
AU - Giacomini, H.
AU - Pérez-González, S.
AU - Torregrosa, J.
PY - 2013/11/1
Y1 - 2013/11/1
N2 - 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. © 2013 Elsevier Inc.
AB - 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. © 2013 Elsevier Inc.
KW - Bifurcation of limit cycles
KW - Global description of bifurcation curve
KW - Homoclinic connection
KW - Location of limit cycles
KW - Primary
KW - Secondary
UR - https://www.scopus.com/pages/publications/84881669233
U2 - 10.1016/j.jde.2013.07.006
DO - 10.1016/j.jde.2013.07.006
M3 - Article
SN - 0022-0396
VL - 255
SP - 2655
EP - 2671
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 9
ER -