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摘要: 给出了平面高次系统具有不变实不可约达布多项式的充要条件. 在此基础上利用代数方法, 根据平面二次系统表达式中的二次多项式来判定系统平衡点是否有闭轨线环绕, 进而指出闭轨线内部的平衡点必须具备的一些条件.Abstract: This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbitwas deduced for quadratic system.
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