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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
9 ~; u: }! h U\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
, v# ^' {. \9 k& [/ I\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = + v3 {& r% D& C7 U5 i4 q( s3 }: L
1 - \[Gamma]a - \[Gamma]m; V5 ~2 X. v @- D
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;$ N- w4 E" M* u# L
\[Theta]m = 0.75; \[Theta]s = 0.9;% v* Q. M* s d6 Y4 {
gRate = 0.02;* a8 P: T+ [1 \4 B9 @
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;" h- i' E, z4 c4 T
ps = Bm/Bs; pa = Bm/Ba;
2 Q9 p7 V; W4 U3 W7 u2 }$ T\[Delta] = 0.03;
* s7 H/ |& e4 i* WB = \!\(TraditionalForm\`\*5 u$ n& G5 n, ]
FractionBox[. G, C7 A G; X- V& L" j _
RowBox[{
1 V/ W G) f# v8 y, j( M3 w% }RowBox[{: R8 b" m6 P6 A4 S
RowBox[{
9 p8 A1 O: @$ G5 cStyleBox["(",
% X" ]) \5 n8 _+ WSpanMinSize->1.,
) s. U( ?5 S8 {( D) bSpanMaxSize->1.],
* w( R: A- m8 n: BRowBox[{"1", "\[Minus]", "\[Alpha]"}], " P8 ^1 t% E0 g9 l/ M6 S
StyleBox[")",8 r( ^ H- p+ y" j. e' l3 @6 T2 B
SpanMinSize->1.,1 ^5 |: A/ ?6 d; {* G
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], # G% ?4 {8 ]2 v& q# X
"\[Alpha]"] \[Minus] \[Delta]\);! _6 x" p* B5 m; v7 ~
cap = 10;
3 N6 J; S- g, ecsp = (pa*cap)/ps;1 q& S j) L& W$ z
D = ((1 \[Minus] \[Alpha])*
5 g6 w8 O% e+ h gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
) I; o/ H; |0 _! @\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;+ ]. i6 E5 [0 @# z
Print["*** Initial Values ***"]
4 k' ^- g/ Z6 S7 `' ^4 TE0 = 1.5;$ L5 D# j1 `! p$ }$ |( ?: L* E0 |
K0 = E0/B;
. S+ l. f* B8 W# y% U) K$ T( ~, ~hm0 = 0.25; hs0 = 0.25;(* initial values *)! ^6 @$ d1 ]: l& ]0 H
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;! z8 Q: _7 X( I
xm0 = (B*\[Gamma]m^\[Epsilon]*" G* B( K. Z; Q& J* F2 {2 o/ I9 X
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(8 Z, L4 I5 L g! D, g' E2 I
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*0 V; ?' n# U+ [5 S/ E) c
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*+ `3 P5 w* o. K* \; O
hs0^\[Theta]s)^(1 - \[Epsilon]));
% W8 }. w! ]) z, p% Oxs0 = (B*\[Gamma]s^\[Epsilon]*(ps*! P d% ?/ X* k/ `% c8 P
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(0 L1 s" R2 R% N3 o! [# g
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*% W8 f9 s# c, I* a* e' {" e
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
: _: ?/ q) ^5 l# h" Q0 [4 Z) I( ` hs0^\[Theta]s)^(1 - \[Epsilon]));" K% \1 F( k1 Q% E
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], ! c$ q j& H, r6 x
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], , j B- E1 `2 e& @0 o
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
, l9 e" ~$ S8 y; @TT = 100;(* end time *)
* k' a( J$ T# w$ Q9 I(* Solve differential equations *)4 A0 G4 E7 @3 S' z: V
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
* N3 O9 L1 Q# o$ v0 k" D# @ xs[t]*( (1 - xs[t]/
j, t1 V+ b- q% u. W B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - 1 A0 C1 k' w% r8 _2 n0 M
xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), , v$ ]# c" ~1 s8 Q. E6 {
xm'[t] == (1 - \[Epsilon])*
" D% r) W4 L' v* E xm[t]*( (1 - xm[t]/8 S7 W% v% E) D8 j( i* D; _- X2 U' W. H0 r
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
: ~: |; F* V' t7 q, J4 A xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
/ p4 w# L8 R, }' s* G- v 1) ), \[Eta]m'[
5 F' _1 s, t* R; O5 l1 A, Z& r t] == \[CurlyPhi]m*
2 D, C+ F* [. Z5 U$ U& ?& ? xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[0 N2 {6 t- P$ N' r9 r
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], " m3 K* o$ S' ]/ W1 ?3 p
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
% B3 L3 B5 y; }+ o8 |/ _6 ^ hs[t] == \[Eta]s[t]*K[t],
" R) G$ E7 W8 T5 s Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
7 ~% c7 F7 X' B; n2 K" u1 d7 b* \\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 g8 B. D8 x6 x hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*7 K8 i6 l% U8 l8 F1 S+ V- @
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
; Y7 k; V5 g; p+ Z" t hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*7 x Q: Y1 Y' _+ U( n7 Z9 e
cap)/((\[Gamma]a^\[Epsilon]*pa^(* ~+ w: E+ L5 ^+ ?" r4 S
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*$ L* r) U4 R6 d5 G
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \' H# F7 ]6 D P
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*8 l' D" M- E. j
xm (t)), / Z* o- P) M5 S8 W; A
Sm[t] == (\[Gamma]m^\[Epsilon]*
1 c6 q- `$ f) D" W, u6 g& U* N hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(7 o$ b2 `) ~$ W% ]% \& G% r: K7 k1 Y
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" V! p3 |! ?) P0 W: T ?' F
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*" n3 u' L$ l9 [' X# @& [
hs[t]^\[Theta]s)^(1 - \[Epsilon])), + ? |- D1 k2 c
Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
2 k5 E( g: Y6 ~- W+ X2 o hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
( d6 L$ s% [3 W. l! a3 u' _ 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
: W: f2 b0 M: X. ?# X hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
, S: Z! W, L, x/ P6 F hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*0 M3 v. Z0 x9 H& F) i* p
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*! C8 D& K0 E. Q
csp)/((\[Gamma]a^\[Epsilon]*pa^(; G9 O' G6 E) w/ u, B2 m
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
0 n! p& D, b; g" j4 V, k hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
" Z. {1 d4 {3 y% r# X\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*( W) A, Z0 d, d% Y: F/ z
xm (t)), xm[0] == xm0,
/ N- d# I+ [% {. w( q xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, $ O1 v& b* z3 g, i
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
! s" u4 I% @* m5 P4 u 0, TT}]
; i3 t) l! S4 m: \Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
$ K7 J# x8 S9 q x. l* x* n Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, ( M4 L: Q2 x4 S
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]! S0 F% b8 @0 Q- }1 F, m( ?
Plot[{Evaluate[D*Sa[t] /. Sol], o5 ~) q) X: M0 S4 |4 u7 s
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + ' c% E/ Y4 M' j* ^
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
* L8 G, F3 R( n7 S+ M AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, 3 a& R4 F! c$ I1 S& {
PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]9 i# K ~7 ~/ S; x4 ]
/ E, |, B9 ~& Y6 F4 ]( k8 ]- X
) }2 z0 W" a- u% n
* { C5 q4 c6 ?/ y. I1 K2 d, L; x% P/ b- j* V! E
Set::wrsym: Symbol D is Protected.
6 f! v1 V- b& w1 I+ Q: i) C9 O9 M9 F5 R6 M+ Y& `' @
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.}.6 P& Y5 ?, M# K/ `7 R4 K
" Z2 P" j% h- O
9 \7 d7 T: ~4 M1 ~, q7 |/ t5 [
* \; U5 n4 C4 ]% H c3 _# n, d
9 \7 O3 W3 v: F+ M# i |
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