Distinguishing weak focus and center point, determining stability of solution, the method of central manifold and Hopf bifurcation, the theory of normal form are important issues in the study of differential equation and dynamical system.
中心与焦点判别问题、解的稳定性判别、中心流形及Hopf分支方法、规范型理论是微分方程和动力系统研究中的几个重要问题。
参考来源 - 计算机代数系统在微分方程研究中的应用We exhibit calculating formula about direction of Hopf bifurcation and the bifurcation periodic solutions in the first bifurcated TO and so on with norm form theory and center mainfold theorem,Furthermore,we carry out numerical simulated compution with Mathematica.
我们还用中心流形和规范形理论，给出了在第一个分支点τ_0处的Hopf分支方向，分支周期解的稳定性的计算公式。
参考来源 - 具时滞和Holling功能性反应的捕食—食饵系统的稳定性及Hopf分支Local dynamical behaviors of the systems are studied by center manifold theory and normal form method of high dimensional mapping.
应用映射的中心流形—范式方法确定了系统的局部动力学行为。
参考来源 - 多自由度冲击振动系统的周期运动和分岔·2,447,543篇论文数据，部分数据来源于NoteExpress
方法利用中心流形定理并结合平面系统的分支理论。
Methods Using the theorem of center manifold and bifurcation theory of planar system.
利用中心流形约化方法证明了霍普夫分歧解的稳定性。
By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.
在此平衡点附近建立中心流形定理，并证明中心流形有空间指数衰减性。
We give a center manifold theorem in the neighbourhood of the equilibrium point, and prove that the center manifold is exponentially decaying.
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