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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \; ], V4 q" |* I1 y3 t3 k7 ]
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
7 Q! |: R. [- M9 Q: m+ |8 a\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = 1 }% {' K& u/ }: [/ D
1 - \[Gamma]a - \[Gamma]m;# L T0 [4 {0 K) L1 s1 ?. t
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;7 L' B7 z; r3 P2 j6 E# I
\[Theta]m = 0.75; \[Theta]s = 0.9;7 c5 f7 W* C( Y' \
gRate = 0.02;' z' E% [8 C# u7 `/ e: y
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
; T* G, ?6 q5 g, n, Fps = Bm/Bs; pa = Bm/Ba;! |3 K7 i5 y: L [! j5 z. i
\[Delta] = 0.03;9 L! _+ ^+ R; _3 ]* b
B = \!\(TraditionalForm\`\*2 @. _' j. f0 R
FractionBox[2 d5 F0 }1 w8 T
RowBox[{/ R- Q8 J P& L% l* }
RowBox[{
3 p+ v r! y- \) C; GRowBox[{& b3 I) }; k* |7 v
StyleBox["(",: R: G) r/ D5 w6 F% E. U" O
SpanMinSize->1.,
; C n+ R: Z6 J5 i0 tSpanMaxSize->1.], " p+ h+ q7 S& d: B7 b6 @
RowBox[{"1", "\[Minus]", "\[Alpha]"}], / a* l: x0 @" j6 \4 x# [
StyleBox[")",# J2 J& |3 b* T& H
SpanMinSize->1.,
J8 L: ]& W6 e e$ A/ g- D% [SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], + i: C9 ]7 h0 X, ^3 `8 R# _; Z
"\[Alpha]"] \[Minus] \[Delta]\);
+ o) L4 M# F r$ N, ?2 I5 w j% Z- X3 Q2 jcap = 10;( X1 i4 o5 D, F) _5 [& y( x" |
csp = (pa*cap)/ps;
& ~; F0 }* F% ZD = ((1 \[Minus] \[Alpha])*
) P1 S& N3 E4 _: K9 N, q gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
' O' }1 H9 e+ U# y; `\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
; a( l5 C; x- l# LPrint["*** Initial Values ***"]$ e: p4 ~, o! Z) b0 K
E0 = 1.5;- p# J' P5 T- a# |! B, O" g
K0 = E0/B;3 `0 l s a9 v$ \
hm0 = 0.25; hs0 = 0.25;(* initial values *)) b' Z/ a x+ P8 q6 `- Y; t
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;1 w, m* ?! L6 l' U
xm0 = (B*\[Gamma]m^\[Epsilon]*2 | r! K( ^( e! J! f, P
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(1 q' v# |- m3 C9 a ~1 F
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*' O9 H2 a+ z0 h1 W- k: V
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
2 B& F" s" a1 x9 m hs0^\[Theta]s)^(1 - \[Epsilon]));& N8 ^+ E$ Z- w' m3 a* Q0 x" [' s
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*. h: P. |# K7 e, I
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(& O0 F( J4 m: z
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
, R4 U) k5 U) q; D hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
\4 ]- p) o1 q4 M hs0^\[Theta]s)^(1 - \[Epsilon])); V9 k4 \4 r0 W; d, g8 t3 m9 T
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], ' e+ |3 p1 ]$ w I9 T
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
6 O9 x3 |2 f) }% i9 W- O+ e ", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]. T+ S* i* `, n* H
TT = 100;(* end time *)- s5 W4 [5 ^7 |5 x i0 ~8 ~# w! F; }* W- N
(* Solve differential equations *)
- D7 O% v. d, b7 d% rSol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
% E! ~/ _3 N0 p0 B xs[t]*( (1 - xs[t]/1 s0 l/ g7 Y- |8 J( V9 @( e
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
9 v: j N3 L" ]3 G2 W7 ^1 N xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), 9 r% ?2 G* W& ?# ]# N5 ]2 k1 {& T
xm'[t] == (1 - \[Epsilon])*
3 j0 O) C$ {( q xm[t]*( (1 - xm[t]/
% @3 |/ ~+ z$ H" x; E; w2 @ B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
; @% { p; W4 V; _3 z; {" e5 V8 Z. ]4 m xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 0 }2 A3 w) w; q) B8 u1 l2 o
1) ), \[Eta]m'[( D- w- i' Z/ s- a
t] == \[CurlyPhi]m*
q& I0 O' _. q5 _3 N; k# u0 | xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
U, E' G; _3 L. S t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
! s& g2 m/ u. S/ n+ c* H; D" X K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], & `1 z8 U. Q. b) i
hs[t] == \[Eta]s[t]*K[t],
# \& P+ l0 g- E. K! b8 a$ `( H$ b Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
5 o+ u& f% m- C+ ^+ z; x\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*: ^$ F1 W3 s& G( j$ i1 a* h
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*, f4 i, D9 m. W# p
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
0 o& r! i) U6 W1 q7 A2 E6 W, u hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
' K6 o9 z& F1 K cap)/((\[Gamma]a^\[Epsilon]*pa^(' y- s& a8 r' o+ X( W& l( u$ f
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
* @: J! g# _* O& C! [ hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \ L7 u/ s- [6 j
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*5 J! h% Z0 ^/ }: x. y2 @. {
xm (t)), 9 k8 G5 D( |5 I% K, p G- Y7 {
Sm[t] == (\[Gamma]m^\[Epsilon]*
# s( m8 K! R+ `! D# q hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(8 \9 t `# A4 J0 M; Z
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*5 T+ m: H+ e+ v$ C) Z3 F
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
2 n4 f( K* k9 S. u0 f t U4 q8 ]5 ^ hs[t]^\[Theta]s)^(1 - \[Epsilon])),
2 {& z+ h! Z2 b1 z, X. l Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*( @9 {+ u: o4 R- @# f& v- j1 G# X
hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(( \9 m6 w2 e" T5 k7 s v8 q8 |
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
* G, m" n5 G2 {+ B, K hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
* h9 [$ y! J3 g& k: T hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
8 j1 k( H/ x7 q7 ]1 ?; T2 \- M hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
/ `: @5 v2 }3 H# k3 ] csp)/((\[Gamma]a^\[Epsilon]*pa^(
; r D# v- U1 _+ `- _$ @ 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*# `9 ?9 h8 T7 c( M+ w, _ T4 G- S
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
2 {, d4 R: L6 ^+ J" @\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*' V6 f" v7 k% d1 F: a- s5 I
xm (t)), xm[0] == xm0,
D$ P: z& `" e5 M' h; ?' K v2 G% O xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, ; A9 A$ P' s$ g0 j, x) u2 I& V
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
m$ W2 m+ s% Y! y. z. S 0, TT}]8 H5 {4 k! M, x3 X, c
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
, O. ]! j1 v+ |. ^6 w( t9 f( @* \ Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, & M2 V- c. E/ K7 x: i4 S2 a8 w
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
% h5 @; f. n% f, }* s1 S3 R- rPlot[{Evaluate[D*Sa[t] /. Sol],
+ m% l& B& n5 W+ ~5 _7 G8 h% v" R Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
$ p: v; g" m+ q' B) s n& t gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
+ z* K* i1 s7 o, }8 h AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
2 J% I- G r+ y! j PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
- r$ B; S# P+ t) u/ f" K. O) z1 C& z
, Q/ p ~: a- i% J" Q- _
! D/ |1 ?5 ^) x: O2 u: l& C0 W# V4 W- m' R9 i: ~. l
{3 n8 \. ]) n2 z Y
Set::wrsym: Symbol D is Protected.* T1 w, Q6 T! V0 W5 b
" t5 o2 k5 p! |6 }4 \, Y7 H
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.}.( m# D) |1 y3 D N8 D: w
$ e/ c+ Y7 [6 D4 G; K! d, J* l5 @9 e' K+ S) ~! J j" a# S
. c4 h `) Y: h, @* U3 ~0 |2 W1 W4 L0 s4 T& ~
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