1、a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a6a14a7a19 1a20a22a21a23a25a24a25a26a25a27a29a28a31a30a33a32a22a34a22a35a37a36a22a38a22a39a22a40a37a41a22a42a22a43a22a44a37a26a22a45a22a46a22a47a37a48a22a41a22a49a22a30a33a50a22a51a22a52a37a45a22a42a22a49a22a30a33a53a34a22a54
2、a22a55a22a56a22a57a22a42a22a43a22a44a22a58a37a39a37a59a37a60a37a61a37a62a64a63a37a65a37a30a67a66a37a32a37a34a37a23a22a24a37a26a37a27 x4 a28a69a68a22a70a72a71a69a30a64a73a22a51a22a46a37a47a48a25a41a25a49a25a39a29a71a31a44a25a40a25a41a25a42a22a43a22a74a25a75a22a76a22a44a22a62a77a52a25a78a22a79a22a80a2
3、5a53a22a34a22a81a22a82a22a83a25a84a22a85a22a86a22a87a25a88a22a89a22a90a22a91a22a92a25a93a22a42a43a25a44a25a94a25a95a25a55a25a96a29a71a31a97a25a23a22a42a22a43a29a28a69a44a22a98a22a99a22a44a25a100a22a101a22a102a22a103a25a104a22a39a22a44a22a105a22a106a25a100a22a101a22a30a77a107a25a108a22a42a22a43a22a44
4、a25a105a22a106a109a25a110 a62a112a111a25a27a25a113a25a24a72a114a69a30a116a115a22a27a22a68a22a83a22a117a22a118a22a44a22a78a22a74a22a119a22a120a37a52a22a121a22a42a72a122a69a107a22a108a22a44a22a123a22a111 a109a37a110 a113a22a123a22a111a22a42a49a22a62a111a25a27a25a124a25a125a22a26a25a126a22a127a22a128a2
5、2a129a37a130a22a94a22a95a22a44a37a42a22a43a22a30a132a131a37a133a22a134a22a100a37a42a22a43a22a62a132a52a37a126a22a42a22a43a22a30a33a135a22a63a22a94a37a95a22a136a137 a30a132a26a25a138a25a139a25a140a22a73a22a51a22a46a37a47a22a48a22a41a22a49a37a56a22a57a22a141a22a44a37a58a22a39a22a59a22a60a37a61a22a62a3
6、3a63a22a65a22a30a33a53a22a34a22a139a37a54a22a90a22a91a22a92a37a93a22a42a43a25a44a25a129a25a142a25a30a112a143 a109a22a110a22a144a22a145a37a146 a141a22a44a22a58a22a39a22a127a22a128a22a136 a137 a65a37a147a22a148a22a44a22a94a22a95a22a62a149a52a22a26a22a150a22a83a22a151a22a152a37a140a22a153a22a74a134a22a
7、100a22a42a22a43 a109a22a110 a44a22a123a22a154a22a30a64a23a37a155a37a134a22a100a37a42a37a43a22a44a37a124a37a125a72a28a157a156a22a128a37a120a37a150a22a83a37a44a37a158a22a51a37a62a159a31a160a25a161a25a162 a40a25a41a25a42a25a43a25a61a22a163a25a54a22a55a22a164a25a165a22a26 a162 a40a25a41a22a42a22a43a25a1
8、66 (a167a24a25a26a25a27 x1), a111a25a27a25a81a25a168a25a169a124a25a125a25a26 a162 a134a25a100a25a40a25a41a22a42a25a43a22a166a22a30a170a63a22a171a22a81a22a26 a162 a134a22a100a22a40a25a41a22a42a22a43a22a166a25a44a22a94a22a172a22a158a22a51a25a89 a161a22a162 a134a25a100a22a40a41a22a42a22a43a22a61 a144 a
9、62a64a68a22a173a175a174a22a176a22a177a22a178a22a179a22a180a22a181a22a182a22a183a175a74a22a70a22a184a22a668:dx1dt = a11(t)x1 + + a1n(t)xn + f1(t);. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .dxndt = an1(t)x1 + + ann(t)xn + fn(t)(1.1)a44a22a42a22a43a22a166a22a30a64a141a22
10、a44a37a185a37a186a37a74 x1; ; xna44a22a134a22a100a22a98a22a99a22a30a64a52a37a187 aij; fi; i; j = 1; ; n a188a74a189a22a190 I a144 a44a72a191a69a192a22a98a22a99a22a62a133a22a38a22a193a22a194a22a42a22a195a22a30a64a196a22a197a72a122a157a198a22a113a37a199a201a200a69a202a37a203a37a62a64a202x =0BBx1.xn1CC
11、A ;dxdt =0BBdx1dt.dxndt1CCA; A(t) =0BBa11(t) a1n(t)an1(t) ann(t)1CCA ; f(t) =0BBf1(t).fn(t)1CCA :a204a22a42a22a43a22a166 (1.1) a54a22a55a22a136a22a194a22a133dxdt = A(t)x + f(t); (NH)a205 a28 A(t) a113 f(t) a41a37a206a37a131a37a133a208a207a37a209a37a210a37a211a212a113a214a213a37a215a37a216a37a217 .a2
12、18a155a37a219a37a220a37a221 f(t) 0a222a30(NH) a223a165dxdt = A(t)x; (LH)a141a22a131a22a133a224a215a22a216a22a177a22a178a22a179a22a180a22a181a22a182a22a183 . a65a218a155a22a219a22a220a22a221 f(t) 6 0,a225 fi(t); i = 1; ; n a140 a188a226a22a133a22a227a222a30 (NH) a131a22a133a228a213a22a215a22a216a22a1
13、77a22a178a22a179a22a180a22a181a22a182a22a183 .1a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a6a14a7a46a22a229a22a230a22a231xi(t0) = i; i = 1; 2; ; na156a22a54a22a136a22a202a22a133x(t0) = ; (1.2)a205 a28 a74 na232a22a233a122a69a198a22a30a225a122a69a198 ( 1; ; n)a44a22a87
14、a22a234a22a62a69a55a22a171a22a235a22a236a22a89a72a122a69a198a37a30a188a74a37a70a233a122a69a198a22a62a133a37a38a37a195 a160a37a237 a194a37a165a201a122a157a198a37a113a37a199a238a200a157a184a239a61a37a44a239a40a239a41a37a42a239a43a37a166 (NH) a197a37a240a37a241 a110 a30a64a32a37a34a37a196a37a197a26a22a
15、45a22a202a22a203a22a113a22a242a22a243a22a62a131a25a26a25a199a29a200 (a244a25a245a25a246a133a25a129a25a130a25a199a29a200a69a44a72a122a69a198 ) a98a25a99a25a74a248a247a25a249 (a250a252a251a179 ,a250a247a25a249a251a179 , a47a47 ) a44a25a30a253a70a25a44a25a74a22a141a22a44a22a254a37a26a22a121a37a255a1a0a
16、188a74a1a2a4a3 (a250a54a25a40a25a30a250a2a1a3a37a54a22a40a37a30 a47a22a47 ) a44a6a5a253a26a25a199a200a69a98a22a99a22a44a8a7a22a209 (a250a8a9a180 ,a250a11a10a1a12 ), a74a22a70a22a52a1a13a22a26a22a121a22a199a72a200a69a98a22a99a22a30a31a141a22a44a22a105a37a121a22a255a4a0a22a74a4a14a22a199a200a69a44a1a1
17、5a22a158a22a255a1a0a22a44a4a16a37a99 (a250a48a22a41a22a30a250a1a17a1a18 ); a131a22a26a22a199a72a200a69a98a22a99a1a19 a233a74a21a20a1a22 (a250a24a23a1a25a1a26 Ia27 a174a1a28a1a20a1a22 ) a44a22a30a64a70a22a44a22a74a22a141a22a44a22a254a37a26a37a121a4a15a22a158a37a255a4a0a246a165a22a44a4a19a233a74a4a29a
18、1a30 (a250a23 a189a22a190 I a144a26a1a31a1a29a1a30 ) a44a22a62a66a22a172x =0BBx1.xn1CCA; A =0BBa11 a1nan1 ann1CCA ;a204a22a202jxj =nXi=1jxij; jAj =nXi=1nXj=1jaijj;a65a1a32a22a220a22a131a22a133a72a122a69a198 x a113a22a199a72a200 A a44a34a33 , a156a22a131a22a133a24a35a22a209 . a143a1a36a1a37a72a71a39a
19、38a22a30a41a40a4a42 a145 a71a157a66a4a43a4a44a121a22a140a22a47a22a61a1a45I. jAxj jAj jxj.II. a46 B a156a37a74 n n a199a201a200a157a30a64a204 jABj jAj jBj; a129a37a206 a237a4a47 a85a49a48a132a63a239a99 m, a128jAmj jAjm.III. a50a1a51a140a22a47a22a61a1a45a46 y a156a22a74 n a232a22a233a122a69a198a22a30a64a204 jx + yj jxj + jyj.IV. a46 x(t) a74 n a232a122a69a198a22a30 a160 a t b a144 a2a1a3a22a30a64a204Z bax(t)dtZ bajx(t)jdt:a52 a531. a143a1a36a1a37a72a71a39a38 a145 a16a22a140a22a47a22a61 I-IV.2
