On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system
The authors study limit cycles of the near-Hamiltonian \(\mathbb{Z}_4\)-equivariant polynomial system \[ \dot x=H_y+\epsilon P_5(x,y), \quad \dot y=-H_x+\epsilon Q_5(x,y) \tag{1} \] with the Hamiltonian \(H=-2 (x^2+y^2)+(x^4+y^4)\) and \(P_5, Q_5\) being some polynomials of degree five. Using the methods of Hopf and heteroclinic bifurcation, it is shown that system (1) can have 13 limit cycles.
scientific article; zbMATH DE number 5757564