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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
, g" F% x6 Q8 B\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]) ]- _3 H2 v7 k
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
( z; B' v* g' u& s$ l6 R 1 - \[Gamma]a - \[Gamma]m;- f3 x3 b7 T3 a, D5 i @4 W8 k
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
; T6 _7 F4 r6 B* |# T& l\[Theta]m = 0.75; \[Theta]s = 0.9;; t) ?3 `) G! L" Z0 L4 T
gRate = 0.02;
V) O- w9 u4 q+ k9 ]Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
2 a; E+ W; F: p9 [8 @+ y: V% Hps = Bm/Bs; pa = Bm/Ba;
3 \0 X' {1 ], |\[Delta] = 0.03;
- Z F7 v( ?/ o! N5 dB = \!\(TraditionalForm\`\*9 T' L7 G, o( c* u: i
FractionBox[ S& w/ g( p& A* Y! H/ J9 l% m
RowBox[{* C8 K, ]9 h" M$ T' N
RowBox[{
& X3 u: j+ P2 Z/ s! \3 x5 z2 {7 KRowBox[{4 z: J+ l/ {1 T+ ^+ c; A3 l! m
StyleBox["(",# E' h) P: R( _
SpanMinSize->1.,
T* A4 z7 w; l. ^SpanMaxSize->1.], 0 a7 s. n) L# F' n* r. {( ]
RowBox[{"1", "\[Minus]", "\[Alpha]"}], 3 N5 H4 H1 Z5 `! f8 @
StyleBox[")",8 I! W% D. @ ]8 G
SpanMinSize->1.,
: J: q! y; @3 ?SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
: f2 v* o# q( l* ~" n9 O; P6 b "\[Alpha]"] \[Minus] \[Delta]\);, i; e- |9 d1 `3 a" T5 M) O
cap = 10;9 c/ U; O5 p/ g( p6 e, b5 ^
csp = (pa*cap)/ps;& G: T8 N& |; C1 H- [
D = ((1 \[Minus] \[Alpha])*/ X% A7 I4 F& F! I- _2 a
gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);* _6 m2 q. x) |
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
$ e; t0 I' ^+ D. R3 a! P4 ?! X! r. l6 wPrint["*** Initial Values ***"]$ Z K& S g4 S/ R6 d! p: l
E0 = 1.5;
; a7 \+ C0 L; WK0 = E0/B;
6 F# j1 l# C; R6 Khm0 = 0.25; hs0 = 0.25;(* initial values *)
* A& N8 H9 p) |\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;4 V$ J8 X8 k/ @6 K3 x) T& y
xm0 = (B*\[Gamma]m^\[Epsilon]*& d* i# Z! |9 a) r+ V
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(8 n, z A0 P# l, y( @9 y" N, X
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 x R* B/ @& x9 Y: p6 j s hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
- F* i, \( q7 [! M. c1 s hs0^\[Theta]s)^(1 - \[Epsilon]));
% f w [! H8 O2 q' r% txs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
, `0 m5 U W0 t5 w hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(5 X, N; V; G5 {: O% V" s- {! C
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*: `6 ^% Y7 T3 _/ L
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
J+ p) F0 ^% G& ^* X hs0^\[Theta]s)^(1 - \[Epsilon]));
5 D* a" o$ t* l6 m# HPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
# o9 \( }! M( u* j ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], * X$ t# u4 C' w5 Y
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
& ], D; w1 M7 J) I2 ATT = 100;(* end time *)6 g- G0 [3 s" s9 j* n% n1 v: t- [& s
(* Solve differential equations *)
% O0 I6 P5 r8 s( Z. {+ B0 \$ U1 {Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*1 ^1 r5 `! t* b9 |) N4 ^- o
xs[t]*( (1 - xs[t]/
2 E* a% H* Q, P/ ^: ~$ w3 r% z B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
. A5 t% i; d2 N6 \% v& i xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), 3 i0 z" U! [5 P
xm'[t] == (1 - \[Epsilon])*
" r+ U3 z! v8 Y. Z xm[t]*( (1 - xm[t]/
7 s( t. w* S' \* U& p, v B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
4 }& l1 k' C* g; J/ [! K xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - u4 |; b* G0 Y0 V3 r8 x
1) ), \[Eta]m'[; z7 R3 [" O- ?+ ^/ f) t
t] == \[CurlyPhi]m*
" w& y1 Q" P: [4 T- r xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[7 a+ l- t% t; v$ _! Z4 K( d
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], - i3 k: r% |: O- x
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], 0 k+ K+ j: a% y7 S v- A
hs[t] == \[Eta]s[t]*K[t],
$ B% L7 u( U7 R Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\& Q5 v4 ?. X5 T4 J
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*0 K* E |% q0 y% O8 @
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*( Z/ d, w y6 ~, y: b+ Z
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
8 j7 \9 I% X+ x6 K8 R hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*) u2 z8 \+ h( u0 U: d
cap)/((\[Gamma]a^\[Epsilon]*pa^(
# d. c9 S* z/ q) P/ z3 v+ r( i 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]** E. l7 l% U- G
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
9 O4 Y5 v1 f( {5 U: n! N: O4 \\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*0 R* Y; G6 I; b: h& V/ i" y; I, S
xm (t)), ; d) g8 a7 Z$ o% c! y
Sm[t] == (\[Gamma]m^\[Epsilon]*. p: L: B( j) q, Y' u
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
5 H3 G6 O2 C: W 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
7 A. u+ e4 V+ G# v4 m% \6 x0 l hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
) W; R# a5 Q9 f/ N3 ]& T4 ^8 M- D( h7 { hs[t]^\[Theta]s)^(1 - \[Epsilon])), 0 d+ j+ L8 C9 _! Q3 U
Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
5 N7 I2 h) l- e% y: {& f hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
_5 \& l5 u" u* ?$ K7 ]; @ 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*8 e$ ] K# R3 J' Q- d1 i
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*; G: J- l/ ^8 {# k
hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*! S1 |5 w, e. d9 C; f' \% v Y
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
: _8 _* I+ |' r% f8 ~+ z csp)/((\[Gamma]a^\[Epsilon]*pa^() i: F, Y$ R8 ]& v: {& [% k, } k
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
5 R" [3 o) z2 _6 L' M. @7 i) o, k& I6 z hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \. d6 y& W. w; K
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*7 S' f2 F" I$ q( z
xm (t)), xm[0] == xm0,
' [- U: ^7 i0 _" `- c. y$ L. t( a xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, 8 t1 s0 @+ Y4 p+ I0 V
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
! ?$ e* _$ U4 G' ~# r 0, TT}]/ Q- l$ f' q3 N& R
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], $ B! w' @& |4 D' x
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
' o5 h$ ^7 I8 y7 M PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
! N/ K; X6 v) `& ^4 O1 P8 \Plot[{Evaluate[D*Sa[t] /. Sol], - x M5 x, u$ V1 j
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 3 a+ E2 A) s1 E1 j
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
5 c" I; U' ?, n; B% } AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, 8 d0 m; y. t; u5 K
PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
- [5 F5 H: `) X3 n, f! Z: [. W: |' c8 ?, t& e9 O* T( T
6 Q. F, o, V6 g, [2 n
- k4 I- t4 u5 `( f" b+ T
; l* A: X; S# }/ KSet::wrsym: Symbol D is Protected.
3 \5 N" J, Y& n8 p: J& A! T% A6 m+ t/ p0 H& a$ x
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.}. a Y7 c+ s# u0 D* q K( Y
7 E, ]6 ~% ?1 _+ K: S$ L( B+ P: H* P2 t1 j2 a) a
! l2 u# T+ {5 ? N# }
$ Y% s5 A. y" b |
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