On the Number of Limit Cycles Bifurcated from Some Hamiltonian Systems with a Double Homoclinic Loop and a Heteroclinic Loop
2017 ◽
Vol 27
(04)
◽
pp. 1750055
◽
Keyword(s):
In this paper, we study the number of bifurcated limit cycles from near-Hamiltonian systems where the corresponding Hamiltonian system has a double homoclinic loop passing through a hyperbolic saddle surrounded by a heteroclinic loop with a hyperbolic saddle and a nilpotent saddle, and obtain some new results on the lower bound of the maximal number of limit cycles for these systems. In particular, we study the bifurcation of limit cycles of the following system [Formula: see text] as an application of our results, where [Formula: see text] is a polynomial of degree five.
2018 ◽
Vol 28
(01)
◽
pp. 1850004
◽
2015 ◽
Vol 25
(05)
◽
pp. 1550066
◽
2016 ◽
Vol 26
(11)
◽
pp. 1650180
◽
2018 ◽
Vol 28
(03)
◽
pp. 1850038
2014 ◽
Vol 24
(01)
◽
pp. 1450004
◽
Limit Cycles Near a Piecewise Smooth Generalized Homoclinic Loop with a Nonelementary Singular Point
2015 ◽
Vol 25
(13)
◽
pp. 1550176
◽
Keyword(s):
Keyword(s):