为更好地指导教学，文章还对如何准确、有效地利用对称性简化二重积分的计算作了进一步的探讨。
To give better advice on teaching, futher discussion, is made on how to simplify the double integral operation with symmetry, precisely and effectively.
从理论和实例两个方面，指出了对称区域上二重积分计算中易出现问题的原因，并给出了避免错误的方法。
From the theory and examples, the article points out why in the symmetric block the calculation of the double integral is easy to go wrong and offers some methods to avoid errors.
给出了完整的分支图和各区域上的相轨线结构。结果表明，非对称项引起二重极限环分支和分支曲线的复杂性。
Moreover, a formula for calculating double limit cycle bifurcation is derived. Finally, the complete bifurcation diagrams and phase portraits are obtained.
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