The global bifurcation of a cubic system (Q2431954)

The authors show that with proper selection of the parameters and for \(\epsilon > 0\) sufficiently small the close to a Hamiltonian system \[ \dot x = y, \quad \dot y = x(1 - bx - x^2) - \varepsilon y (a_1 + a_2 x + a_3 x^2 + a_4 y^2) \] can be made to exhibit five limit cycles, two nests of two cycles each all surrounded by a large cycle.