Using algorithms of computational algebra we prove that at most eight
limit cycles can bifurcate from any center or focus at the origin of the cubic system x =
̇
λx + i(x − a−12 x2 − a20 x3 − a11 x2 x − a02 x ̄2 ). That is, an upper bound for cyclicity of the
̄
̄
x
origin of the system is eight.
