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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \4 c% B" P- d1 Z, x
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]& a/ B" v: _0 d7 l" }
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
2 c, O3 j: [* K' B 1 - \[Gamma]a - \[Gamma]m;
, y3 x$ W; R) } Q' _3 O5 \- M\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;: s, V7 R w! Q6 y3 T
\[Theta]m = 0.75; \[Theta]s = 0.9;3 U7 i" l% {/ d2 I" j' }' z2 i# N- k
gRate = 0.02;" S- D" \8 a, @6 @
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;0 U, K* z# L, K/ q' W" s: y
ps = Bm/Bs; pa = Bm/Ba;- e% C& Z1 u( L) w
\[Delta] = 0.03;! E- `4 X# q5 j( a
B = \!\(TraditionalForm\`\*
& M" l9 r9 ~9 a4 e$ @+ AFractionBox[
2 |2 i" q0 N: BRowBox[{
; n& x# c& H% j; x' f" yRowBox[{
7 F: |0 t% g+ Z" m- u, j* s+ H) z9 ZRowBox[{
' y0 U4 x6 u% z% m+ ^3 fStyleBox["(",3 ]6 W( d- Y" P2 a8 g. r% f- v
SpanMinSize->1.,
" P/ `* u) I6 Y7 QSpanMaxSize->1.],
! t( ]' b7 n5 P$ m1 D$ i1 YRowBox[{"1", "\[Minus]", "\[Alpha]"}], + O( R# \* w; ~6 v
StyleBox[")",
1 I: i( `8 \4 ~8 I6 F9 _3 QSpanMinSize->1.,. L0 e( c& M; d; i( k% @
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], : b( f2 W2 g* P; Q2 X
"\[Alpha]"] \[Minus] \[Delta]\);- ?9 T7 z: ~/ i) O
cap = 10;
6 V/ t3 m5 r0 ]4 o$ G1 O) ]csp = (pa*cap)/ps;' E/ _- e) |0 a4 m2 t
D = ((1 \[Minus] \[Alpha])*
9 \5 O6 K) l1 e- M. {* U7 { gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
& {" ]8 i) X/ R9 ?4 b1 {* o5 N3 a\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
. `- C* p% t) sPrint["*** Initial Values ***"] v+ M; c3 e, `8 M& F6 ?, `2 i
E0 = 1.5;3 ?( D! L# l" p) [, ^
K0 = E0/B;$ P: n2 E8 ^8 Q p
hm0 = 0.25; hs0 = 0.25;(* initial values *)2 F6 [* P3 r. P
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;7 K7 W) S0 n8 ]7 \' b+ V6 W) Z- k
xm0 = (B*\[Gamma]m^\[Epsilon]*! M0 A" I2 [: Z$ t
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
8 F0 q/ [& x, z% R- E$ D* x: p2 m0 B 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*7 _% v* ^; w6 M5 |* c9 Z
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
" g5 n" j2 R, M7 c& Y$ u hs0^\[Theta]s)^(1 - \[Epsilon]));
7 {$ q7 J; l2 c; J$ ?xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*/ ?& B" K6 W" I
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
* ^% F* e. K; Y2 N( E) E; [: q 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
0 ^' N7 z% X6 ?+ p4 \$ m' y hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*1 }8 J4 c0 R, C7 |2 m2 x( a8 B
hs0^\[Theta]s)^(1 - \[Epsilon]));' ^2 _, `+ [& D
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], / l- ~3 Z0 R2 S' F
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], 1 a. d/ T+ D: \; K: |! x8 _
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
4 ~: f" }8 Q) ETT = 100;(* end time *); M9 [0 c" }0 M! E
(* Solve differential equations *)
# e3 E& d: t9 S; ZSol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
4 y3 c+ F5 j8 B: R+ f xs[t]*( (1 - xs[t]/
9 }6 Y2 V8 E& X% t4 M; n B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
& x7 r0 C2 Z; ~" Q% p xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), , A9 @( r. Z& b I! |3 }% P5 K+ Q
xm'[t] == (1 - \[Epsilon])*$ @2 J+ e7 W5 U' x4 u% ?5 m8 H
xm[t]*( (1 - xm[t]/% }- y% H P/ V I. l8 E2 C V6 U8 ?
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - 8 ^. |( S; `& _! U& { f
xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 5 s. U% X: Q# G4 k3 D: z
1) ), \[Eta]m'[
9 h a4 Q" {# G! W t] == \[CurlyPhi]m*
2 |% d) J9 H' Q' H, O7 z xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[; |4 Q# M* }$ Z: B( J( G \) p& d
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
+ C8 P% b$ `7 l# _ f; r# D6 O K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], 7 D' x, \* o' p2 j7 B% G
hs[t] == \[Eta]s[t]*K[t], 8 @4 @- q- ^0 Q2 [+ m
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\ f1 U' i/ n* c; A! ^& ^; o
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" C8 r% k* Z" F
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*7 b8 S, c7 [; Z. ?0 ~
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*; e( ?$ y# x6 l" @
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*5 S' |" z3 V4 X7 A6 h8 h
cap)/((\[Gamma]a^\[Epsilon]*pa^(
7 C. c4 p! k2 t/ L. P8 W" F 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
- G r) O# s7 l2 c! h hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
: A0 M2 g2 E9 v1 c" b1 R# t* s\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
( G7 n! k! d, I) C xm (t)), 3 X6 h, [. G$ r; C9 x- E# V
Sm[t] == (\[Gamma]m^\[Epsilon]*/ S* B3 {# E* c2 S6 r6 ~/ I
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^( f; r5 F. p6 J6 p9 B
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]** K* K: O0 s+ Z1 A) ?5 r
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
$ X) T2 b; h" @ hs[t]^\[Theta]s)^(1 - \[Epsilon])),
: V! {! e: U+ g* q4 U& D& P# ^ Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*0 x6 P# w7 C1 t5 I
hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
: v# X! D. ?; N) P: G$ |# u 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
6 G( X. J, G. Z% C hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
2 N6 ~9 i& W6 G" e* T hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
9 K) \) Z9 e3 k- X( ` hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
* t! C; D! {* @ csp)/((\[Gamma]a^\[Epsilon]*pa^(
- d& _. x/ ]6 F3 f! v1 | 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*& g3 \; o5 K' C" W* g, G
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
) N& S6 D7 a. I. F) S5 O\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*& T; U$ f# N, e8 c( ^9 |
xm (t)), xm[0] == xm0,
# m+ I4 P( V4 s5 w xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, * R4 y$ V) D% {+ Q
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,& q2 {# S& r7 v3 H7 R
0, TT}]" K- ]" y) ^9 z0 c8 ?' l
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], ; e3 m4 M$ Y$ p8 C
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
3 H3 z" i' ?4 H+ g, O* r0 e% c PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]3 C! N8 q# D. U x8 m
Plot[{Evaluate[D*Sa[t] /. Sol], 6 W( Q& @% g. S9 ^
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 7 d; V1 d: w4 p/ `" K/ r6 Q$ R
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, $ h" @0 H/ o" @
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
3 c" ]4 i9 a+ f5 O7 k8 g PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]- x( s/ `9 }' y; X3 X
0 M% z0 A( d6 S$ ?, k& i2 i8 }/ v, e
3 X5 Q9 m; x" _" D5 d
. B& G' d& o; X3 l; rSet::wrsym: Symbol D is Protected.# ~) `. B- E- I
( Z1 h6 a0 T5 W& o$ m2 lNDSolve::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.}.
% y/ ~/ A) j7 U8 i, k; D0 e( ?8 f/ W# q8 k8 y
7 G: n3 A7 m# R4 b8 ^/ s1 a
0 e- f. E0 P7 y4 ?3 ^: a2 Z) y9 ]1 I; j; B. X8 i) w
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