On the number of limit cycles of a cubic near-Hamiltonian system
By using a suitable first order Melnikov function the authors investigate homoclinic bifurcations for the following near-Hamiltonian cubic system \[ \dot{x}= y + \varepsilon P(x,y), \;\dot{y}= x - x^2 + \varepsilon Q(x,y), \] where \(P(x,y)\) and \(Q(x,y)\) are cubic polynomials of \(x, y\). It is proved that this system can have \(5\) limit cycles with \(3\) of them being in a neighborhood of the homoclinic loop of the unperturbed system.
scientific article; zbMATH DE number 5574113