CAJ | 학술논문

通过讨论一类E3^1系统x=y，y=-x＋δ＋a4x^3＋a6xy^2＋a7y3的定性性质，引用微分方程几何理论，构造了正不变集，指出了系统存在正（负）无界解，同时应用Hopf分支理论及指数稳定性分析了系统的极限环存在性与不存在性．
통과토론일류E3^1계통x=y，y=-x＋δ＋a4x^3＋a6xy^2＋a7y3적정성성질，인용미분방정궤하이론，구조료정불변집，지출료계통존재정（부）무계해，동시응용Hopf분지이론급지수은정성분석료계통적겁한배존재성여불존재성．
The paper discusses the qualitative theory of a kind of E3^1 system x = y , y =- x + δy + anx3 + a6xy2 + aTy3. By quoting geometry theory of differential equations, we structure positive invariant set, and point out that there exists positive (negative) unbounded solution of the system. The existence and nonexistence of limit cycle for the system is given by introducing Hopf bifurcation theory as well as stability of index theorem and combining with differential equation geometry theory.