The number of limit cycles for a family of polynomial systems

In this paper, the number of limit cycles in a family of polynomial systems was studied by the bifurcation methods. With the help of a computer algebra system (e.g., MAPLE 7.0), we obtain that the least upper bound for the number of limit cycles appearing in a global bifurcation of systems (2.1) and (2.2) is 5n + 5 + (1 − (−1)n)/2 for c ≠ 0 and n for c ≡ 0.