考察两阶微分方程组: f(x12x2) (3.29) g(x 令x=x作坐标平移,不妨仍用记x,则平衡 点x的稳定性讨论转化为原点的稳定性讨论了。将 f(x1X2)、9(X1,k2)在原点展开,(329)又可写成 =f(0,0)x+f(0,0)x2+0(x2+x2 d=8(0,0)x+8,(0,0+0x+x2) 考察(329)的线性近似方程组: h叫x+br (3.30) =cx, +dx 其中: a=f(0,0)b=f00)c=gx(0.0)d=g21(0.0)考察两阶微分方程组: 1 1 2 2 1 2 ( , ) ( , ) dx f x x dt dx g x x dt = = (3.29) 令 ,作一坐标平移,不妨仍用x记x’,则平衡 点x o的稳定性讨论转化为原点的稳定性讨论了。将 f(x1 ,x2 )、g(x1 ,x2 )在原点展开,(3.29)又可写成: o x' = x − x 1 2 1 2 1 ' ' 2 2 1 2 1 2 2 ' ' 2 2 1 2 1 2 (0,0) (0,0) ( ) (0,0) (0,0) ( ) x x x x dx f x f x o x x dt dx g x g x o x x dt = + + + = + + + 考察(3.29)的线性近似方程组: 1 1 2 2 1 2 dx ax bx dt dx cx dx dt = + = + (3.30) 其中: 1 ' (0,0) x a f = 2 ' (0,0) x b f = 1 ' (0,0) x c g = 2 ' (0,0) x d g =