Limit Cycles for the Kukles system

Limit Cycles and Invariant Parabolas for an Extended Kukles System

A class of polynomial systems of odd degree with limit cycles, invariant parabolas and invariant straight lines, is examined. The limit cycles can be obtain as a bifurcation of a non hyperbolic focus at the origin as Hopf bifurcations. We will also obtain the necessary and sufficient conditions for the critical point at the interior of bounded region to be a center. 2010 Mathematics Subject Cla...

Centres and Limit Cycles for an Extended Kukles System

We present conditions for the origin to be a centre for a class of cubic systems. Some of the centre conditions are determined by finding complicated invariant functions. We also investigate the coexistence of fine foci and the simultaneous bifurcation of limit cycles from them.

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.

Small amplitude limit cycles for the polynomial Liénard system

We prove a quadratic in m and n estimate for the maximal number of limit cycles bifurcating from a focus for the Liénard equation  x+f(x) _ x+ g(x) = 0; where f and g are polynomials of degree m and n respectively. In the proof we use a bound for the number of double points of a rational a¢ ne curve.

A quartic system with 26 limit cycles