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, \. s' N% T0 j% w. A% S- r
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]3 q: B, m' u# S. P$ N8 @4 S
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = 1 r; j' n/ U7 e
1 - \[Gamma]a - \[Gamma]m;
) }! [0 L' H2 n8 L7 D \[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
! h/ J: U" d" v+ L, x- x0 m& ~ \[Theta]m = 0.75; \[Theta]s = 0.9;
5 s% l: O; B( S/ R" {7 d9 N gRate = 0.02;
0 d# \0 y S) l8 O3 r Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
4 ]/ i* B, r7 q; A1 z4 g ps = Bm/Bs; pa = Bm/Ba;& Z- j, Z& c3 f5 o- M& k9 y3 p
\[Delta] = 0.03;8 k5 {4 ? t; e! z# {
B = \!\(TraditionalForm\`\*
# T+ N) h& D' @$ W. U+ v& H FractionBox[
! O4 }$ d) n! L8 h RowBox[{
; k" H4 C0 L) k( e" j RowBox[{& o: Z) z" `7 @7 `5 J6 L# o, ~- N
RowBox[{
3 P2 ~: K% l$ K. `5 X StyleBox["(",
" V ^* Y( y- l/ ` e0 N, A, v SpanMinSize->1.,
) N0 z1 {1 h2 O0 F SpanMaxSize->1.],
) m4 A8 ~2 |0 t5 b# a( a RowBox[{"1", "\[Minus]", "\[Alpha]"}],
) k' Y* w0 c1 A/ X StyleBox[")",
4 ^6 f% \% p4 T SpanMinSize->1.,
{- |; D7 W) w, Y! G SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], % W7 ~* }* ` h$ }0 p2 [
"\[Alpha]"] \[Minus] \[Delta]\);
! o% n/ Q& K- r0 q' d+ i cap = 10;
& D: ?( V4 x. d& Z k csp = (pa*cap)/ps;2 G+ F# J1 K0 H0 b4 s% r
D = ((1 \[Minus] \[Alpha])*: T1 `6 t& _8 {& H$ Y3 i! Q0 Q0 Z
gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);: ]( ~5 a9 \, Y8 x6 k% e
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
; H5 Q# @" i, {+ J Print["*** Initial Values ***"]5 t5 U$ g# ?, d! d6 R& n
E0 = 1.5;
9 `- X9 \9 b8 y! K6 T, X K0 = E0/B;
/ @1 u2 G) V. e) {0 f) R hm0 = 0.25; hs0 = 0.25;(* initial values *)0 M- B" k w. m5 S. Z% e+ x; Q
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;1 @7 S6 I+ m/ A6 Z" S! N c
xm0 = (B*\[Gamma]m^\[Epsilon]*9 d1 p" D N7 c$ J9 j0 @1 c. e3 F
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
2 i! k- {1 L" r& ` 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
0 C* l! ^+ h( v; Q3 Q9 V hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
. }% F: i/ Z! o5 E hs0^\[Theta]s)^(1 - \[Epsilon]));/ O w4 s" R" D6 q8 U
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*5 J) {2 `7 a6 J1 ^2 e7 m* Q8 h& a
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(% d) C- H2 q2 a( q9 P% m0 W
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*. l" t5 ^' i! ]: O6 t9 k# u
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
7 M' r0 H' _+ L3 H% l, A; B' H6 A& v hs0^\[Theta]s)^(1 - \[Epsilon]));
' i) W2 z$ V" g- z$ W+ n) t Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], ) m( n. ~* L6 c& h: O/ t3 E
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
! p/ v( F8 f% c( H+ J! @ ", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
, t2 b! a1 J3 ^0 g3 j TT = 100;(* end time *)
( c3 w" J1 [. z; [ (* Solve differential equations *)2 s/ Z3 S6 k/ l
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*8 g/ ]2 R/ h! w
xs[t]*( (1 - xs[t]/
8 @, j- }# R9 O( E. Q m" E% V B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - @$ y3 h9 f! H% c- y1 U; X# G
xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
( Q7 P6 r, r/ }- t& E: l- }4 c xm'[t] == (1 - \[Epsilon])*) p8 c. d8 \2 _7 K) a9 T- }
xm[t]*( (1 - xm[t]/' j: N. m o* g& }7 c. Y
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - N* C( g4 l3 e' x0 F
xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
! n* ^8 z$ m+ ?5 e" N2 p* ^6 k 1) ), \[Eta]m'[
8 G+ \! |' S* [, ` t] == \[CurlyPhi]m*& O& R/ Q7 A7 ?8 |# o0 [
xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
* Q; L' P5 j! R- d: Y5 _* p t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], 0 V k' A2 `, t/ J
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], 3 `5 D8 t2 z& ?; ~% y
hs[t] == \[Eta]s[t]*K[t],
4 ~' V/ h2 d" ]2 b Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
! D* g# V* Q# m4 B! S: `" {/ T \[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*3 x5 V2 k) R9 U' ~3 g9 T, S5 @5 U, V
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
- t+ n0 g, p, m7 a( O hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
' ^* m) D- p% T9 v2 n hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
! |1 i) o' K; Z G cap)/((\[Gamma]a^\[Epsilon]*pa^(
+ x9 U. m# F: Q! I; d 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
- `; q7 @6 ^ U# H! r hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \3 B) ?; z/ B/ }& Q
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*9 X# d) w8 C) i/ Y! m# x
xm (t)),
# r- \+ _' W# Y5 `8 }' w* N5 V Sm[t] == (\[Gamma]m^\[Epsilon]*) U( ^! m1 w0 o2 a4 \
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(, h: b) D5 ^- F9 V& J8 X
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
5 _1 m: J Z' p" ~' p1 w* U hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
l% b) y, b5 r8 C hs[t]^\[Theta]s)^(1 - \[Epsilon])), 2 c. V. R* x+ k& Z9 a
Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*, f" e: V7 Z; J" Q' w
hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^() r& Z+ y$ P3 a2 P7 G
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*; I z I% @- n. J n$ R
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*% e/ }5 n* R& u$ h: l$ t5 P
hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
9 b$ {% w4 u" m: t% ]7 L+ Y hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*, [! b) L3 Q$ u0 A1 w! c
csp)/((\[Gamma]a^\[Epsilon]*pa^(6 U' D4 `5 O5 ?* z+ b
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*! l; h. a8 A/ ^
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
7 O4 Z! l7 Y$ l0 | \[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*+ K/ U t( Y5 \4 w8 V$ e
xm (t)), xm[0] == xm0,
' M8 n1 f4 L" }+ w- B# ~4 k1 y9 H; J xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
! ]: ] E0 {0 c5 ~( |/ V K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
9 K' }7 B7 R5 q, e5 } 0, TT}]) ^/ l! L6 p8 D
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], ! R- u4 C, ^$ R9 `
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
y/ e4 _: T& K6 d PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]7 u/ Z! n0 m U
Plot[{Evaluate[D*Sa[t] /. Sol],
! s8 G L& t7 Q# n6 S) W% V3 { Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 5 W' ]3 `% X/ q2 {! ]
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
0 l2 ?1 p+ s& H3 a6 j7 \ AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
4 b4 W; ]" I+ B, S4 s/ C PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
" d f5 u" x! `3 h ; w" P" i3 ~5 t) l: [
, o4 W, }6 F0 j0 N8 { S0 ^
/ X/ ^7 ~( f: o8 _2 y$ Q
9 O) I. p' e2 n6 ?. n! d Set::wrsym: Symbol D is Protected.
2 B! g$ A. U- ]* ~7 k1 |# D
* O* [, e. J! y* V 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.}.
2 a9 @1 O- Y$ h2 O6 G # D9 k: O, \+ F: ^. X
8 K6 T: Q' _1 @. `5 K S + e2 }# X& e! _! e/ T
7 B+ I" ?, Z% {' o
zan