Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop (II)

Bifurcations of limit cycles for a quintic Hamiltonian system with a double cuspidal loop

“…For all real constants α, β and γ the sharp upper bound for the number of zeros of the Abelian integral I(h) defined in (6) for h ∈ (− 1 12 , 0) is two including multiple zeros. Theorem 2.…”

“…In [5,6] we have investigated the bifurcations of limit cycles in the Lieńard systems of the form ẋ = y,…”

Sharp Bound of the Number of Zeros for a Liénard System with a Heteroclinic Loop

“…For example, Wang and Xiao [16] concluded that the number of limit cycles in the system bifurcating from period annulus is at most three. Qi and Zhao [17] considered the Liénard system of type (5,3), [18], Asheghi and Zangeneh [19] considered the Liénard system of type (5,4), and Sun [20] studied the limit cycles of type (7,6) with a heteroclinic loop connecting two nilpotent saddles. In this paper, we intend to study on a following Liénard system that is a small perturbation of the Hamiltonian vector field:…”

Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle

“…There are abundant results for weak Hilberts 16th problem restricted to Liénard systems of type ( , ), especially for = − 1, such as types (3, 2) [16], (4, 3) [17], (5,4) [18,19], and (7,6) [20]. More details of the relative researches can be seen in [21][22][23][24][25][26][27][28][29][30][31][32].…”