"! #%$&('*)+(,-"*.0/*1$*2 34 #5)3 #%76#9814 #5: 4.3';-0<!3 #5=.4 : '3 # ,-"*.0/*1$*2>(8 #5)@? *#5). A! #%$!#5=87$*2B?*.02=2#%(=.3'C D*: 3=.$ (; 3E dx = 0.12 x − 0.0006 x 2 + 0.00001xy dt dy = 0.08 x + 0.00004 xy dt dx 1 1 = 0.12 x 1 − x+ y dt 200 12000 dy 1 = 0.08 x 1 + y dt 2000 , 3B. (, FFFFFFFF"GH E <(. I*D*:(3=.$C, dy / dt . "!$*.0=. 6*' 8I! #%$!$#5=.$3'B$7"(: )+&#A$*2J>3%?78C;(K7$#% $6# , . L)+:(4 @)A$#%@? !? ($*2<M :*)+&#N$*2<>O3 O8C,+ $L3IPC; P(P(P(P(Q(> 8O. dy / dt .0/*$#%3 &(' G .0B. 4* 3 #98"3B+*.0/*7$*2B>(8"#5)M. !$*.0=. 6(; E RS(:A#%3$*2B. 4 #%*3 $*2B8". 3' )A$*-!$*.0=. 6*' 8"? !? (T$*2B(:*)+&#$*2B>C; UI.0$*: J7#5)$*2J>(8C, dx / dt . 77'$*/ . *=.47 D*:(3=.$3 ?7I D*: .0'0. & #5.0: )O(:*)+&#A$*2J> . V P(PC; -)A*3 A3BWJ(.4 6#J : )+&#$*2BA. (.0=.03'(63'0:((, .0B4*$ 6#5/(AV P(PC; X-:*#5#5)A$#%(, " D:(3=.$ G=H E9, if dx 1 1 = 0 and x ≠ 0, then 1 − x+ y = 0 or 12000 − 60 x + y = 0 dt 200 12000 Y4*(,N. Z[! 3% [!(3*4*(,N2$#\3 (8Z/ . 6]!$*. ( G >C,N8(E9,N.0O/($ ]$]]'0. 3 ?3'$(/(. A'0. +&$*">73 ?8". 4 #%*3 AW "B. 4 #% 3 (; 12000 − 60 x + y = 0 ^+ 3 #I(3A'0. 18_&*/ . 1$_. (4 #% 3 1#53 !(.?*'08`&*4*3 :* x ≈ 200 1 − 1 x ≈ 0 3 ?_.0 200 .0)+!('0.`3"?*>bac?*"3'0)A$*A! #%$!$#5=.$3'$N>(8C;dRS(`&*/ . (. (/N!$*. ("$*2"`8eW(.4 e. #%3 !(.?*'08". 4 #% 3% A. ? ! ? (T$*2B#%3=.$$*2T4*$ *=3%($*2 x term and xy term ; 2 RSW$*'3 !"$*2. (*/*#%3'B4 :*#96". "! 3% !3*4". *. ).0'3 #+$"":*!**.? F ? $*W"3 ! $*2TV"?*.0)A *.$(3'2$*:*(3. *AW$ +*:*! !$#5B. A'0. ( 12000 − 60 x + y = 0 ; RS#%*2$#%(, D*:(3=.$ A3 #%34*$ $!#%3=.$")A$ ?**'; 2B8$*:A ! 3% !(3*4*$*2T3 &$6?*.02=2#%(=.3'C D:(3=.$C,*6(. *.0BW+&!3/( WWW; )A3C; ! :; ?*: a )A*' 6(. a ! 3% a W! 3 (; ()' &(E dx = 0.15 x − 0.0002 x 2 − 0.0006 xy dy dy = 0.2 y − 0.00008 y 2 − 0.0002 xy dt 1 1 dx = 0.15 x 1 − x− y 750 250 dt FFFFFFFFFFF(GH E dy 1 1 y− x = 0.2 y 1 − dt 2500 1000 "(. D:(3=.$C, .02 dx / dt = 0 and dy / dt = 0 , ( x, y) = (0,0), (750, 0) or (0,2500) & 4*3:* >73 ?873 #%$ F */(3=. 6 : )+&#9 ; UI.0$*: > 8I#9),(&$*I?*>bac?*3 ?7?8bac?*3 #%'$*/ . *=.4 D*:(3=.$ "3 ?" D*: .0'0. & #5.0:*)L!$*. ( G >C,(8(E G PC,(V P P(E9; "(. D:(3=.$ GH E9, .02 y > 250 dx / dt < 0 ,A3<. (,e(:*)+&#N$*2I> ? 4 #% 3% (;+K7$#% $6# ,A8O43 . 4 #% 3 V P(PC,* $A(3T6(:(3'0'08C, +(:*)+&#$*2B>7? 4 #% 3 3%?A.0BW.0'0'(&*>(=. (/ : . ?(; 2 x > 1000 dy / dt < 0 ,T3+. (,TI(:*)+&#7$*2+8`? *4 #% 3 (;TY$W+6# ,T>_/($ $ PC,* $A3T 6(=: 3'0'08" :*)+&#$*2B8"W.0'0'C4*$ 6#9/(A$ V P(PC; RS(:A. "! (3 +!34*(,(3'0'(63' :(A4*$ 6#5/(A$ G PC, V P(P(E9; U7"6(3'0:($*2B>". 6#98)A3'0', 8&*/ . $4*$ 6(#5/(A$V P(P#%3 !(.?*'08C; Y 4*(, >"W.0'0'(&*'0.0). 3 ?A3 ?A8W.0'0'(&:*#96(. 6 ?(; T3*4 : )+&#$*2B>73 ?8)A3*/(3=. 6*2=2 4B$*3*4 7$*# ; RS#%*2$#%(, D*:(3=.$ A3 #%34*$*)+!*=.0=. 6)A$ ?**'; 2B8$*:A ! 3% !(3*4*$*2T3 &$6?*.02=2#%(=.3'C D:(3=.$C,*6(. *.0BW+&!3/( WWW; )A3C; ! :; ?*: a )A*' 6(. a ! 3% a W! 3 (; ()' 278$*:eW+3 ("$N eN/(#%3'3% *W+#9e3 ?` $'0: =.$ M$*2I?*.02=2#%(=.3' D*:(3=.$*(,+2$# *>3)+!('(,(! #% ? 3$# F ! #%*8I)A$ ? *'B3 ?74*$*)!*=.0=. 6")$ ? *',I8$*:I4*3 7#%*2#+"2$*''$*W. (/ &$ $ C; B'*)A(3 #58"?*.02=2#%(=.3'C D*:(3=.$*3 ?+&$*:*? 3 #9863' :(! #%$&('*)+ U7#5.0=&(8$*84*A3 ?J. C#5.0)A3 G Rd(. &$ $ ". A. AK"3- 3 #9(. (/ (# ; E