In this paper

we first reduce the system of equations dx/dt = a_1x + a_2y + α_1x2 + α_2xy + α_3y2 dy/dt = b_1x + b_2y + β_1x2 + β_2xy + β_3y~2to three standard forms(Ⅰ) dx/dt =α1'x2 + α2'xy + α3'y2

dy/dt =rx + sy + β1'x2 + β2'xy + β3'y2

(Ⅱ) dx/dt =α1'x2 + α2'xy + α3'y2

dy/dt =x + β_1x~2+ β2'xy + β3'y2(Ⅲ) dx/dt =α1'x2 + α2'xy + α3'y2

dy/dt =β1'x2 + β2'xy + β3'y2

by p=a1 + b2 ≠ 0 or p=0

where △=a_1b2 - a_2b1 =0. Then

we obtain following conclusion: When p≠0

we only need to discuss the system of equations (Ⅰ)

andobtain that the stability of the zero solution may be determined by the criteriain §2. When p=0

we immediatly obtain that the zero solution of the system ofequations (Ⅱ) and (Ⅲ) is unstable. Therefore

the discussion of the problem is simplied.