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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
; S0 y0 A5 ]4 _! a% i\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]7 a6 Z. S' @! e, F" P
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = " J1 x, m0 N$ P* V" r( M
1 - \[Gamma]a - \[Gamma]m;# V9 S$ O R/ m: y
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
7 y2 U! x4 Q5 F0 v# l\[Theta]m = 0.75; \[Theta]s = 0.9; z( m& z1 B; N7 p* u- ]& U
gRate = 0.02;1 W [. r% Y. Y% z$ M5 `# I0 p
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;. Q" y* O/ e8 W( a, I; _/ N, ]
ps = Bm/Bs; pa = Bm/Ba;$ S! v0 |7 q; p, M7 d2 o
\[Delta] = 0.03;6 m! N( X+ _% e" R
B = \!\(TraditionalForm\`\*
6 F$ {( ?: l# ^3 P1 W/ t0 uFractionBox[
. B2 C1 V. p% x$ n9 jRowBox[{5 t1 k; ~4 p6 I
RowBox[{ r- c0 t: I- X, W5 X
RowBox[{
0 G+ Z2 q/ Z9 c5 TStyleBox["(",# J0 g3 G# S" s0 W- f
SpanMinSize->1.,- k8 x7 H) R0 A0 \% ]- m f
SpanMaxSize->1.], ' {9 _% T5 X* j
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
6 |, ?6 T2 `9 mStyleBox[")",0 l# n2 v4 r1 z3 P" @( @5 K
SpanMinSize->1.,0 t, V `7 Y# t7 s3 G% q# [
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], 3 V; Z% n- Y6 @
"\[Alpha]"] \[Minus] \[Delta]\);8 e! s3 B; I2 }5 G! @
cap = 10;
3 L- s3 C+ p' P9 Qcsp = (pa*cap)/ps;
, ~# {. m Z2 i# c4 RD = ((1 \[Minus] \[Alpha])*
! {7 D7 U8 y8 J; x& w2 B, \" }& | gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
' p1 P5 X, H, g" n\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;! Z+ X; c' w {! v
Print["*** Initial Values ***"]
+ s. X# h: P7 B% ?% oE0 = 1.5;
- j9 |' p4 W7 y2 m2 wK0 = E0/B;
! J% E" a* U( dhm0 = 0.25; hs0 = 0.25;(* initial values *)
0 {* Q6 w6 [# i4 v) M9 c\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;3 X( p h$ k& r. K9 \
xm0 = (B*\[Gamma]m^\[Epsilon]*
2 F' B [9 y% U1 m6 r1 W hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(* i8 b$ |+ q$ J* i. N$ Z, G
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" A/ J, V9 @7 V# T" b
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
6 v8 c8 P, m/ r! U5 P2 L hs0^\[Theta]s)^(1 - \[Epsilon]));9 n% M7 B& M/ e ]
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*2 c' h+ { G. ^1 o
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
' v; v6 `6 Q0 |4 D 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 ]! V: g( w4 q0 I- O; o hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps** [. \3 R/ E1 }3 g6 k# A; C7 f. a
hs0^\[Theta]s)^(1 - \[Epsilon]));3 z$ m3 A M8 i) {
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
6 j9 q4 z" O2 x. ~/ n$ f, s4 l ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], $ Y2 W1 s7 Q- T% e2 I
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]2 O3 O: K z* h0 ]9 U7 D
TT = 100;(* end time *)' ?# g2 T( d4 j. o V) P* m
(* Solve differential equations *)% z: S7 r* z- w v3 t
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])** e7 q( N5 v$ J
xs[t]*( (1 - xs[t]/0 ^- Y* A8 s# L8 d% a
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - % k6 X8 W% s7 H$ U; @
xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
0 T1 v' u9 x# K$ ?9 ]5 x xm'[t] == (1 - \[Epsilon])*, H/ s {5 ?6 B
xm[t]*( (1 - xm[t]/+ q1 k9 e' V) @# M. I, Q, o3 z; c
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
5 q; s+ U. M$ \0 d* ~3 h5 m xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
* w! _& d6 }2 x9 _ 1) ), \[Eta]m'[
a) Q, N( L9 J: K# ~ t] == \[CurlyPhi]m*- w9 C( Y' ?* ~1 z7 C
xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
6 \5 }! @9 ~2 J* b" d4 H t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
( e1 Q- C% g. M% \7 J K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], + `! }, [) i! g7 M
hs[t] == \[Eta]s[t]*K[t],
% o e" J! H5 C8 ^ Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
6 ~: |) ]& [+ E\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
M! C! h4 M' G# C C J; g hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*& \1 ]6 F+ d! y5 E% D; h
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
5 q! i& K! v# l/ s$ y. l' q hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
, R1 b K/ a# `/ N cap)/((\[Gamma]a^\[Epsilon]*pa^( B2 ^% i! t+ y
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
+ V+ V9 F5 n5 N4 b# n5 i& I* k6 J hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
; o: ?9 O+ s) F\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*/ y2 [8 T- n- z6 h2 ^; [1 v
xm (t)), $ w4 f& [# a! }2 c5 v9 T
Sm[t] == (\[Gamma]m^\[Epsilon]*
# x* ^1 g$ P: e hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
+ Z9 H3 s0 O0 ? 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*# @" Q9 K ^: s% n+ D! H# V' ?
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
5 M0 K; }, `. Y! J: E1 b hs[t]^\[Theta]s)^(1 - \[Epsilon])),
2 _$ g9 P% z3 ^' E8 @ Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
) p1 ~4 J c: d hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
; q& X' ^$ x. L- a1 L" ?/ z5 E) v 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*: s; D$ B1 ?$ a" B3 X
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
4 Y( k/ d9 u, A( S4 y! Y hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*' c8 i$ H2 ~5 w, L
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*. E* z* z7 I; w9 E$ T0 y
csp)/((\[Gamma]a^\[Epsilon]*pa^(
1 e; J) m; t4 ^2 Q 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*/ e* B$ Z" u- Z9 A( P
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \0 {7 I. I0 a0 }
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
, o7 ?1 L9 o' `( P. s8 k xm (t)), xm[0] == xm0,
: |8 l5 l& v# y8 r; B5 f xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, : U7 H7 m" P; C$ {, f
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
4 E! L( ^& h- } h, ~; u( F 0, TT}]
, e& {" W4 s! c( ePlot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], 5 q9 d3 i* [& r4 X3 V
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
- w$ k2 M& m( E( E3 v PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
7 v1 a8 k) ~# j) HPlot[{Evaluate[D*Sa[t] /. Sol],
! W+ u3 @6 v3 W; b Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + # K$ y' S8 x+ ?- r" ?, k8 j6 w" E
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, 7 x) p. y& _5 p: O2 Z9 m1 y
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
5 [. o c$ i( o$ f9 O+ ~ PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
2 z$ O" T% z5 E: h
* x/ d8 b; q: m. f0 }1 u f; p5 V
/ i& r+ i& c4 _& t2 }1 v% q! d- K6 U4 J1 z) r. H
0 _0 ~1 u7 {1 F+ }$ CSet::wrsym: Symbol D is Protected.( r; o3 D1 V: X' G+ c
% a `) d9 s7 D1 mNDSolve::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.}.) ?! O1 J0 M! c+ L/ ^
6 c: N% L/ ^" b! O& x
' D1 m) a7 R" P }; U: _
/ q5 ^; u- c+ _9 R/ _* B z
7 L) u. _3 _$ T! a9 H- D |
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