In this paper, we consider the system x˙= y (1+ x) 2− ϵ P (x, y), y˙=− x (1+ x) 2+ ϵ Q (x, y)
where P (x, y) and Q (x, y) are arbitrary quadratic polynomials. We study the maximum …

In this work, we consider a cubic integrable system under quadratic perturbations. We then
study the limit cycles of the perturbed system by using Melnikov functions up to order three …

In this paper, we study Poincaré, Hopf and homoclinic bifurcations of limit cycles for planar
near-Hamiltonian systems. Our main results establish Hopf and homoclinic bifurcation …

This paper investigates a class of reversible quadratic systems perturbed inside piecewise
polynomial differential systems of arbitrary degree n. All possible phase portraits of the …

In this paper we study the monotonicity of the ratio of two hyperelliptic Abelian integrals I0
(h)=∮ Γh ydx and I1 (h)=∮ Γh xydx for which Γh is a continuous family of periodic orbits of a …

In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-
Hamiltonian system by using expansions of the first order Melnikov functions. We give a …

In this article, the general Liénard system dxdt= ϕ (y)− F (x), dydt=− g (x) is studied. By using
the Filippov transformation, combined with the careful estimation of divergence along the …

In this paper, we study the number of limit cycles in the perturbed Hamiltonian system dH= ε
F_1+ ε^ 2 F_2+ ε^ 3 F_3 d H= ε F 1+ ε 2 F 2+ ε 3 F 3 with F_i F i, the vector valued …

In this paper, we first consider a cubic integrable system under general quadratic
perturbations. We then study the Melnikov functions of the perturbed system up to the fourth …

In this paper, cubic perturbations of the integral system (1+ x) 2 d H where H=(x 2+ y 2)/2 are
considered. Some useful formulae are deduced that can be used to compute the first three …