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Æ 2003 3 20 100 ¨x+p˙x+qx=0(1) !pq#$%&’(2) !pq#()*+, - ˙x=−y+x(x2+y2−1)(x2+y2−2)˙y=x+y(x2+y2−1)(x2+y2−2)!./01Æ2’3&’456 789u(t):x(t)!; =?@ABCDEX(s)U(s)=s−1s2+s−2FGX(s):U(s)HEx(t):u(t)!?@A5(1)-u=tet:x(0)=x(0)=0I!#x(t).(2)Ju(t)=kx(t),kEKL5MkENOPx(t)$%&’QR ST˙x=2y˙y=−x−x2yUVW3 XYZ[\$%&’]^ (1)˙x˙y=sin(x+y)x−y,(x,y)∈IR2UVuv=2xy+x2_ 7()‘a@A1bcde‘aI! 5(2)b 7 ˙x=f(x),x∈IRn: 7fgy=ϕ(x),ϕ(0)=01MNPhdx=0!i7jkU:y=0!i7jkV1ly=ϕ(x)EUmV!)n‘a@A1ocp dy‘aI!qr5(3)b’ST˙x=f(x)+g(x)u,x∈IR2,g(0)=0J* 7sLϕ(x),ϕ(0)=0lt uvLLgϕ(x)=0w;dϕ(x)xdLfϕ(x)d0[y4z{5UVWhd 7|}sLu=α(x)+β(x)v: 7~[jk!‘a@Az=ψ(x)1ldz‘aI1ST@E Iy4qr˙z=z2˙z2=v W1. g(x)=g1(x)g2(x), Lgϕ(x)=g1(x)∂ϕ(x)∂x1+g2(x)∂ϕ(x)∂x22. ϕ(x) dϕ(x)=(∂ϕ(x)∂x1,∂ϕ(x)x2)