摘要
考察了三维非线性临界动态方程Z.=f(Z),f(0)=0,Df(0)=A,σ(A)={±ω.i,0},ω>0的局部渐近稳定性.首先在非奇异线性坐标变换和时间尺度变换下,将其化成标准形式.之后,运用形式级数法的思想,在f(Z)是解析的假设下,研究了三维自由动态方程Z.=f(Z)的李雅普诺夫V函数的构造问题,给出了确定李雅普诺夫V函数的方法,并得到了判别三维解析动态方程局部渐近稳定的一组充分条件.
The local asymptotic stability of the 3D nonlinear analytic dynamic equation was studied, which is formulated as Z^·=f（Z）,f（0）=0,Df（0）=A, in the critical case of σ（A）={±ω·i,0}, ω〉0. The study consists of three stages. The first is to convert the formulation of the equation into the standard form under the transformation of the nonsingular linear coordinates and time-measure. The second is to analyze the constitution of the Lyapunov＇s V-function and to develop further a method for determining the V-function by the aid of the idea of form-series. The last stage is to obtain a sufficiency condition of the local asymptotic stability for the 3D nonlinear analytic dynamic equation.
基金
福建省自然科学基金(A0440005)
国家自然科学基金(70671045)资助.
