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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \6 V3 M, u% b6 V; v7 e
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
: t5 p1 M' k( @0 x\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
+ }, z3 u/ ]( r* i+ z5 C9 p8 p' d" E# N 1 - \[Gamma]a - \[Gamma]m;
4 O, l, q% k* A8 P% Q; _9 ?\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;4 q( T6 [ N3 X9 G
\[Theta]m = 0.75; \[Theta]s = 0.9;
0 U) U1 w8 [) N% j% j& D: r* TgRate = 0.02;4 |8 ?9 y3 a; q4 Y' n4 A& ?
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;0 m( Z1 [8 ~7 D/ Y) ~+ e* Z! f
ps = Bm/Bs; pa = Bm/Ba;
( m* ~& c' D' m4 h\[Delta] = 0.03;
7 v/ i. H u- Y1 MB = \!\(TraditionalForm\`\*
, c& D, y+ Z7 x2 n1 QFractionBox[* U2 e* X/ m6 t2 o
RowBox[{
! X) e8 j7 @5 h DRowBox[{
- E* p5 E' b8 X0 `7 A# A% wRowBox[{
* K8 t* ?) y M- x; N* m# C* |* GStyleBox["(",
3 S3 L7 r+ B( ~$ U1 U% kSpanMinSize->1.,
$ b n0 C" z9 {% b6 XSpanMaxSize->1.], 8 A0 p4 n0 P/ q9 H0 j
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
u, l( m7 L/ ] C$ `& u1 yStyleBox[")",
0 a0 b1 G7 ?. u% ZSpanMinSize->1.,
) x* d3 d9 F& g7 C7 c( OSpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], & J' V* {7 A" X. H& K* Y* M- m
"\[Alpha]"] \[Minus] \[Delta]\);
( |' X2 V% G4 ]cap = 10;
4 b: d# a% u- D8 _/ L% B' ?* Wcsp = (pa*cap)/ps;
5 y: Z# p0 k+ gD = ((1 \[Minus] \[Alpha])*
; x& i8 r W0 a/ T K t' t gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
9 D# g# h' g) {! n3 H$ w. Y\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;% d5 v# {( j2 Z
Print["*** Initial Values ***"]
2 j* ?, ]4 }/ I1 f/ V0 DE0 = 1.5;
8 k3 U0 F6 e. p9 l2 t. ~K0 = E0/B;
- Z. A' @1 |& ?1 b& O; bhm0 = 0.25; hs0 = 0.25;(* initial values *) o+ b# U: Y# L( [- ~
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
2 j* q6 c. v, Pxm0 = (B*\[Gamma]m^\[Epsilon]*
P- s; [/ t4 ]; f/ f+ u/ S hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^() R5 p. O* R6 W1 D6 ?
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*: ^# ? J( V/ v* f: e _
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
0 _8 O% _, i: b hs0^\[Theta]s)^(1 - \[Epsilon]));9 D5 [7 _. {. _( t; I* W: |' T
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
7 B. S- G, L$ d0 D5 x& ?. f. I, J hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(% W1 |7 `/ S# o
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*( ]- Z5 N2 a3 H5 J$ J7 ]
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
& a' r t( J( _) z0 y" X+ R0 E4 a) r hs0^\[Theta]s)^(1 - \[Epsilon]));
; s, j9 C* n0 l) m3 ]) N2 EPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
' A3 E+ h( | x; i ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], 3 o: X5 A: u4 _; s0 [1 s
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]* p2 {$ f4 c( |$ z
TT = 100;(* end time *)$ Q* z4 E6 B4 [4 l
(* Solve differential equations *)
; b7 x2 N) G! Y( V- |: ASol = NDSolve[{xs'[t] = (1 - \[Epsilon])*+ C9 Y. U: O) \ ^, \" ^( _
xs[t]*( (1 - xs[t]// P$ V! f5 O I7 A( B9 Z1 q
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - * n. B c, L0 p( d" J" ^
xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), , t% @/ l4 U/ Q2 T- l: v
xm'[t] == (1 - \[Epsilon])*
( C, u D8 I- s7 |' N xm[t]*( (1 - xm[t]/' p$ j* ?/ P `5 ^/ Y
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - 3 |" s3 \, V9 b& `
xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
1 J9 a3 V* E9 k# {/ y 1) ), \[Eta]m'[
& B9 A; D6 n( V% U; V3 g+ _( E1 j t] == \[CurlyPhi]m*
/ s, {0 ^# T( n0 G' n% v4 B5 O xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[4 s4 A* w+ v3 K" R4 ]# u- F; B
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], : Y: k1 D0 f$ a: l# n& D7 }
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], & _9 V6 H. W1 J0 J
hs[t] == \[Eta]s[t]*K[t], 5 B& R: k$ g7 j6 h# f
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
+ K$ T/ P4 ?) n3 s* |\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
5 u) v" V5 A d, N8 V0 {3 D1 \% Q hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*- p1 O4 ]6 X" k3 M; u7 q
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*$ Y7 A" ]' B @9 q- n4 b
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa** Z( A `& @3 J2 z5 @
cap)/((\[Gamma]a^\[Epsilon]*pa^(
6 t4 s/ |+ y1 m. p7 D) p( ^# D/ j% t, c 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
1 c+ |+ z* u8 x( O, }5 N hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \4 N5 v4 {' H% k* F+ d: y8 B
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*: N* O& b* u: _
xm (t)), & ^+ A4 p4 a+ ]3 ~ t8 \, ^: j
Sm[t] == (\[Gamma]m^\[Epsilon]*9 \2 @. e! p8 B
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
! c% _' e2 J, ^! ] 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
, ^3 W; d! a* ?5 G/ K9 D hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*+ B- ?' t1 Z9 H! `& [
hs[t]^\[Theta]s)^(1 - \[Epsilon])),
) @% |, v- Y1 F( U5 B* [: j Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
; g/ H+ [# t5 m5 P/ y hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^( ?+ _- u2 N% i8 d# s# y/ _
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
3 R8 K2 m1 `' r; l* O7 A2 m hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*+ o5 X: y. J9 F
hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*- K; k) G, h2 s* h+ W
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
% X) }. u8 w" y9 ^5 @ csp)/((\[Gamma]a^\[Epsilon]*pa^(
3 [& H g! `# |7 ^- e3 ]/ i0 M 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*0 v5 ]$ P) S U3 L9 ^; A( y: g
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \( ]5 k/ I" C" Y8 h0 l
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*% }7 \ B+ p( ~
xm (t)), xm[0] == xm0, ! _0 n* t) Q& k6 r
xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
+ I8 b5 o5 P- L K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
7 O+ W/ W2 b$ \% a 0, TT}]' f: H; Y6 t1 O& y
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
& m. e u; j9 }; j3 W9 U Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
8 q0 V. b. K. P+ o" G, h5 x8 P+ e PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
0 P( C- Z2 L3 S( j! A: LPlot[{Evaluate[D*Sa[t] /. Sol],
- Q$ m7 j) e* F( @9 A6 r" A Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + : }' l( p' ]. D: {) G2 ]- [
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, 4 l4 L5 `3 v2 M, a2 w* H
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
# y4 ^+ o9 u2 _5 H, q& E# H0 F PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
: I3 H8 O6 e E! o' ]8 |& u1 S6 T+ X- L) K e) Y
/ t( ^/ H* e: l0 s) i% R, M0 _
. @4 h% L4 F- L8 \2 \4 ^2 _$ |
+ F F! z+ n+ D
Set::wrsym: Symbol D is Protected.) A' b+ j( K9 M6 S
$ a N! e( k4 l5 c# ?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.}.
8 F0 W% B3 P: i! Z7 G2 `; m5 G; A
; S8 W: Z8 z& }4 P% p- F; Y( ^
; j* l! k0 B8 v. U( A) f
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