Limit cycles for a class of polynomial differential systems

Limit Cycles for a Generalized Kukles Polynomial Differential Systems

We study the limit cycles of a generalized Kukles polynomial differential systems using the averaging theory of first and second order.

Limit Cycles for a Class of Three Dimensional Polynomial Differential Systems

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers ẋ = y(−1+2αx+2βx), ẏ = x+α(y−x)+ 2βxy, α ∈ R, β < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging...

Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems

We consider the class of polynomial differential equations ẋ = Pn(x, y)+Pn+1(x, y) +Pn+2(x, y), ẏ = Qn(x, y)+Qn+1(x, y)+Qn+2(x, y), for n ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. These systems have a linearly zero singular point at the origin if n ≥ 2. Inside this class we identify a new subclass of Darboux integrable systems, and some of them having a degenerate center,...

Limit Cycles for a Class of Discontinuous Generalized Lienard Polynomial Differential Equations

We divide R2 in l sectors S1, ..., Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, ..., l, is defined a smooth generalized Lienard polynomial differential equation ẍ + fi(x)ẋ + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynomials of degree n−1 and m respectively. We apply the averaging theory of first order for disco...