本文借由一阶平均理论，就微分系统{█(■8(x ?=y(x^3+ax^2+bx+c)+εP^+ (x,y)@y ?=-x(x^3+ax^2+bx+c)+εQ^+ (x,y) )，x≥0@■8(x ?=y(x^3+ax^2+bx+c)+εP^- (x,y)@y ?=-x(x^3+ax^2+bx+c)+εQ^- (x,y) )，x<0)┤其中c≠0且4a^3 c-a^2 b^2+4b^3-18abc+27c^2≤0，P^+ (x,y),P^- (x,y),Q^+ (x,y),Q^- (x,y)∈R[x,y]，且deg(P^+ (x,y))=deg(P^- (x,y))=deg(Q^+ (x,y))=deg(Q^- (x,y))=4，P^+ (x,y)≠P^- (x,y), Q^+ (x,y)≠Q^- (x,y)，0<ε?1.在 Poincaré分支意义下的极限环个数上界展开了研究。通过计算不同情形下平均函数的生成函数，验证其在参数特定时的线性无关性，得出当4a^3 c-a^2 b^2+4b^3-18abc+27c^2<0，4a^3 c-a^2 b^2+4b^3-18abc+27c^2=0且a≠3√(3&c)和4a^3 c-a^2 b^2+4b^3-18abc+27c^2

According to the first order averaging theory, the paper studied the upper bounds for the number of limit cycles bifurcating by Poincaré of a segmented Quadratic Polynomial differential system {█(■8(x ?=y(x^3+ax^2+bx+c)+εP^+ (x,y)@y ?=-x(x^3+ax^2+bx+c)+εQ^+ (x,y) )，x≥0@■8(x ?=y(x^3+ax^2+bx+c)+εP^- (x,y)@y ?=-x(x^3+ax^2+bx+c)+εQ^- (x,y) )，x<0)┤ With c≠0,4a^3 c-a^2 b^2+4b^3-18abc+27c^2≤0, P^+ (x,y),P^- (x,y),Q^+ (x,y),Q^- (x,y)∈R[x,y], deg(P^+ (x,y))=deg(P^- (x,y))=deg(Q^+ (x,y))=deg(Q^- (x,y))=4, P^+ (x,y)≠P^- (x,y), Q^+ (x,y)≠Q^- (x,y), 0<ε?1.

By calculating origin functions of averaging functions with different conditions, demonstrating their linear independence based on specific parameters, the upper bounds for the number of positive simple zero points for the averaging functions, also the upper bounds for the number of limit cycles bifurcating by Poincaré of the system has been estimated. When 4a^3 c-a^2 b^2+4b^3-18abc+27c^2<0, 4a^3 c-a^2 b^2+4b^3-18abc+27c^2=0 and a≠3√(3&c), 4a^3 c-a^2 b^2+4b^3-18abc+27c^2