Global bifurcation of limit cycles in an integrable non-Hamiltonian system under polynomial perturbations

Global bifurcation of limit cycles in a perturbed integrable non-Hamiltonian system is investigated using bifurcation method of limit cycles. The study reveals that, for the integrable non-Hamiltonian system under polynomial perturbations [equation (8) in the introduction], the upper bound for the number of limit cycles is [(n+m-1/2)] + 1 when n ≥ m + 2; it is m + 1 when n = m, m + 1; and it is m when 1 ≤ n ≤ m - 1. The results presented here are helpful for further investigating the Hilbert's 16th problem.