- 在线时间
- 2 小时
- 最后登录
- 2020-3-30
- 注册时间
- 2020-3-24
- 听众数
- 1
- 收听数
- 0
- 能力
- 0 分
- 体力
- 5 点
- 威望
- 0 点
- 阅读权限
- 10
- 积分
- 2
- 相册
- 0
- 日志
- 0
- 记录
- 0
- 帖子
- 1
- 主题
- 1
- 精华
- 0
- 分享
- 0
- 好友
- 0
升级   40% 该用户从未签到
 |
Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \" U" I( _/ }: Y0 H5 G3 p4 V+ K
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
! J$ J6 W& J6 g( w: N# J; Z _\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = - g, f/ {2 ?/ I! Z6 i S5 e$ j9 N
1 - \[Gamma]a - \[Gamma]m;
7 Q6 a4 i( ^! a' M; _\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;# w" `" _+ C7 T; q& s
\[Theta]m = 0.75; \[Theta]s = 0.9;5 L$ C/ g" @" ~8 f7 P
gRate = 0.02;. x8 w: ?# Y" u* o* z( T( T1 v
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5; [4 h0 N6 ]* \$ F- o
ps = Bm/Bs; pa = Bm/Ba;
' D( O. }9 g# _# @\[Delta] = 0.03;; a9 O* S, y# t
B = \!\(TraditionalForm\`\* v( M8 ? L$ k! \6 N6 W( z
FractionBox[6 H% l4 j% T" h/ N: l
RowBox[{/ r C) f* V* t% U0 P; ]5 j
RowBox[{$ @, C0 k* \* t( I8 w! c- T' ?
RowBox[{
3 P* n. a! I" uStyleBox["(",9 }7 k# g5 A5 w( m! Z, w
SpanMinSize->1.,
$ p1 O8 [2 e MSpanMaxSize->1.], ! z0 A+ @/ m, k! t6 S
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
9 v2 I5 G/ }+ a* u4 c9 Q) AStyleBox[")",
2 j. H2 Q& h* ^) v& C5 H, J$ C/ D( cSpanMinSize->1.,
, |9 ]; E7 p3 `8 _$ WSpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
! ~0 n" c6 \, I6 o B0 ^$ ~- m "\[Alpha]"] \[Minus] \[Delta]\);, c. I& X$ a# e) W
cap = 10;
\7 S/ P; o5 L$ Q" qcsp = (pa*cap)/ps;
9 \7 V2 w: i" t- U; }3 Q0 TD = ((1 \[Minus] \[Alpha])*
( C% L7 i- b- R gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
, I5 j: b$ q/ r. }9 M\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
# J7 {6 h& k* ?! \' g s. FPrint["*** Initial Values ***"]
- l, U" o! S2 Q% M9 v8 W& }E0 = 1.5;2 @3 C+ }) u" g! y# [* t$ J
K0 = E0/B;
' m/ U; r8 S$ ohm0 = 0.25; hs0 = 0.25;(* initial values *)8 H! Z1 C9 v3 Z6 X
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
# l D! c6 `% Hxm0 = (B*\[Gamma]m^\[Epsilon]*
C \2 L% z) G% u' c& k hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^( ~9 s' I& K5 d/ @# V% X, L
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*3 g3 n6 U6 }; d" H S
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* o/ V* t) X. P" i, j
hs0^\[Theta]s)^(1 - \[Epsilon]));6 [: ?: ]4 u) z: e
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
4 }- e$ @+ }7 }$ n7 M hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(7 b4 t7 `: d1 V1 q
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*: a; r2 B6 e# T7 g$ J$ T
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
5 C5 ?% @8 G1 b hs0^\[Theta]s)^(1 - \[Epsilon]));
4 b* z. i" Z$ E8 S9 Q2 SPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], " B+ A; u3 d$ w& P
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], + C" I/ _8 p$ g+ W, r
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
4 x$ X% x0 B! M5 @$ x: u7 |TT = 100;(* end time *)' c1 g* w9 Q: d# d @
(* Solve differential equations *)7 F1 Q3 A- D/ q) v7 x) r
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*& N8 R, v) f1 T
xs[t]*( (1 - xs[t]/5 X0 I( }. T" L" d0 y3 f: Z
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
. N) `' ]# H" B0 t. a9 m xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
S7 n+ l8 D$ T- z$ q xm'[t] == (1 - \[Epsilon])*9 y; a9 v( T ^
xm[t]*( (1 - xm[t]/
; J/ _% [0 n/ a6 H: k* ^) A4 } B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
* @. t( A; F& k e9 B' H% L" n/ N h xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
' X$ s: o! J5 L- w% R 1) ), \[Eta]m'[+ X, {9 K4 S m5 }9 i2 J5 X
t] == \[CurlyPhi]m*
; h: I: o( F! T xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[) s& s2 k5 `! }1 ^" d
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
2 H" j! m, D( |. M K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
9 k/ y1 K4 r5 C/ L% Q! F hs[t] == \[Eta]s[t]*K[t], 9 h* e. x/ i8 w! F0 I1 A3 }. O0 m
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
6 C' ]1 f9 t1 ]5 o3 m\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*+ c" d. N) k1 D4 l+ P# d
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*7 ?; W2 ]3 N- d0 a$ b: D
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*& J! T# z) @/ \8 I6 }1 M
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
2 u0 D& q: J+ J. l2 K" @4 g cap)/((\[Gamma]a^\[Epsilon]*pa^(, b) A! r/ r: c- R6 w) |8 K
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" T' f+ w" D4 q& ]/ S9 j
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \: i2 u9 d: [1 E. I
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*. k, g$ z" p' ?8 G' A7 u4 ?- \* b
xm (t)),
6 ^7 y7 q! V, J: W* K6 z Sm[t] == (\[Gamma]m^\[Epsilon]** Q& a; Y4 Y/ W$ e9 ?
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(5 Y3 z9 p. P* i6 y0 t! C
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
8 L+ p/ [2 |( w/ B) R8 O6 z* v# L hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
& l; w2 e% g/ F& L2 ]4 a; f. Z hs[t]^\[Theta]s)^(1 - \[Epsilon])),
, |" N% O( H7 u* f! V* K Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*1 t9 Q+ w, l" F( r% B+ s8 V5 Q
hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
" x# d, V; D$ m5 v3 E e 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*' K- M) x6 G/ S/ B$ x9 O% ~- i
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*) c! U2 b: E6 N# q" E [) M# A$ X) N
hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
+ V" O# {$ X1 `+ I9 M+ c [& k8 V hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*5 n; s0 u4 k1 F3 T) f. }
csp)/((\[Gamma]a^\[Epsilon]*pa^(
P. \' h9 |, N! _. n 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*9 K% e; H& d4 p: g% A* Y
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \5 N- h: k) ^$ W- x5 h) D0 a
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
. \* D0 A& A* u6 x' ~0 ] xm (t)), xm[0] == xm0,
# e5 x* n% R) m+ i xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
8 f4 A8 {; s& G) L( q0 E) V K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,6 t8 w) J' o4 K4 k5 M, ]
0, TT}]& R/ g) {/ j" @ A, e
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], 3 ~3 K( }+ `2 v6 V: A& S9 r2 ]
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, 8 d) J' Y' e& V5 K. z
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
; b8 U1 W, P$ EPlot[{Evaluate[D*Sa[t] /. Sol], 2 V2 f8 D$ K0 r) e
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
" ?& G. |7 Y: t+ _; |( Y4 [ gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
, N: [9 k* a' ^1 ?# m' e AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
7 [) |7 j3 k0 J PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
. c1 { v0 H( G
# \+ g. }/ c& Y. t
1 e3 W/ \- I3 D& j/ S3 k
) w6 V% X7 J; b# J- j/ F8 X4 h; b) _$ V- {% E
Set::wrsym: Symbol D is Protected., w+ X+ D$ X) [7 Z# [/ F
4 F! N; }! m( a) M. e. H
NDSolve::deqn: Equation or list of equations expected instead of 0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[t])+0.09 (-1+(2.5 xs[t])/\[Eta]s[t])) in the first argument {0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[<<1>>])+0.09 (-1+(2.5 xs[t])/\[Eta]s[<<1>>])),<<13>>,K[0]==10.}.
$ c2 u0 q' j1 N( h" d# O: d( s: o3 f) b9 B8 U# K% w
- ^+ c3 Q5 ~1 d* t9 [* Q2 N
, [; j) E8 r, y) W5 p0 z
0 V- t x4 f* V3 A3 F0 W* ~ |
zan
|