Weak centers and local critical periods for a $$Z_{2}$$ Z 2 -equivariant cubic system

Abstract

In this paper, we consider the weak center conditions and local critical periods for a \(Z_{2}\)-equivariant cubic system with eleven center conditions at the bi-center. Using the computer algebra system Mathematica, we compute the period constants and obtain the order of the weak center for every center condition separately. Finally, the number of local critical periods bifurcating from the bi-center is given by symbolic computation and numerical computation.