Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \/ L6 Z* Z/ x% m' G3 z% `+ w% S: A
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]] / H' c1 e1 o! r1 i. N' H6 H\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = " q2 q* p' N& c1 c/ U7 i, D8 F
1 - \[Gamma]a - \[Gamma]m;1 t2 M- o+ O4 L s; ]' x8 |& k4 q
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04; 7 D8 Q- q8 O v8 ^; G/ s9 @- L\[Theta]m = 0.75; \[Theta]s = 0.9; . B2 X9 U9 O5 A9 U" a0 o, ~3 XgRate = 0.02;- G+ _4 k- ?9 H
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5; 4 `( t, P! r1 S* o1 O) `' Gps = Bm/Bs; pa = Bm/Ba;3 s# [$ b8 f- t8 E; ?
\[Delta] = 0.03;/ L1 ]2 O/ P$ }) @1 v
B = \!\(TraditionalForm\`\* - n% Z, y x7 E& G8 [- eFractionBox[4 t/ d4 o& D6 s# K6 I6 A& j9 q0 h
RowBox[{ * r: w- Q: M4 A. f' `% rRowBox[{7 A- K# C9 U: j; h3 o' `' `
RowBox[{& }- A. @, J) V5 U0 R8 u
StyleBox["(",3 E: V8 X! }+ \$ j
SpanMinSize->1., * o7 e F; z; F4 iSpanMaxSize->1.], - U9 @- Y9 B, k0 K8 G0 m4 Q4 Z$ u
RowBox[{"1", "\[Minus]", "\[Alpha]"}], " Y, U' R4 n0 J( X$ uStyleBox[")", # n$ }( _8 a6 a; tSpanMinSize->1., - X+ W5 N! f/ H1 P4 q9 ` X; oSpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], * b5 `* r+ |# T' I "\[Alpha]"] \[Minus] \[Delta]\);* R* N' ]" o4 M9 |4 q
cap = 10; 0 B- ~' l. v8 w5 L! d. j7 Ocsp = (pa*cap)/ps; ( [& Z+ L. q- n- o+ H& SD = ((1 \[Minus] \[Alpha])* 0 s1 G v) x/ k6 r gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);) Z3 _" }% ^# n6 ~0 T q1 Y; M
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;4 m L& N! O* M
Print["*** Initial Values ***"]$ g+ I) S, v5 f. {5 y% t! Q9 p
E0 = 1.5; # ?) ~3 Y) l* a+ N) a! K2 xK0 = E0/B;8 |% z) g, f+ v6 P& \
hm0 = 0.25; hs0 = 0.25;(* initial values *)! B3 c/ ]" w8 E7 N- Z7 h H
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;9 ?2 v% Z1 X* `7 W4 u. ~
xm0 = (B*\[Gamma]m^\[Epsilon]*: K& } K- L' v6 {% {
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(4 X6 c" I3 S! O. f
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*1 g, F. C- p2 C5 R
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* 9 K! _( I q& E% g& B; D! j+ D5 Q hs0^\[Theta]s)^(1 - \[Epsilon])); / k+ y5 O$ A8 o0 b8 s* C0 Wxs0 = (B*\[Gamma]s^\[Epsilon]*(ps*/ z4 m ]. u) P$ b3 ?
hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^() _% ^. u, ~( i6 j: Q x7 S1 j
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* ( N$ D& E- N/ F, O5 J hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* " b, J5 F1 ~- w2 D4 z hs0^\[Theta]s)^(1 - \[Epsilon])); ; E8 j$ {: D1 e: F8 [Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], 2 G k. l" ]# {3 k+ O ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], $ O( J4 S& r$ o8 ~/ v# Z, j ", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]] - B' g3 v- g) T5 z5 GTT = 100;(* end time *) ! h/ P i5 `' {1 t( f5 J(* Solve differential equations *)( P+ M# _" B1 [
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])* 9 k5 B5 ^" z0 J f }) r/ S xs[t]*( (1 - xs[t]/* s: F. U* `! Y% p+ b; c
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - ) Z; p' r2 c, m. [2 n0 B) S& B1 U xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), 7 l+ P% X$ N3 G: T4 g" | xm'[t] == (1 - \[Epsilon])* 5 y/ f* Z& ?( i" U$ q2 R; g0 i xm[t]*( (1 - xm[t]/ & G- Q3 e V5 n9 D B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - J/ ^4 A) y6 `! c xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 9 G! ^5 j0 @1 a" f" M/ B$ [( P+ h 1) ), \[Eta]m'[5 Z# E; E9 B; D4 s
t] == \[CurlyPhi]m* s4 P5 w% M. ^+ s; c; a/ r xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[" b; ^9 E6 V! {2 K1 G' |; C
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], - k, ?/ z. o0 y" P" |
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], & }7 V: A& X; f! D- q) A4 S7 Z
hs[t] == \[Eta]s[t]*K[t], 8 H6 g0 |# A/ W Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\% ?, @, ?+ F3 h7 l0 r1 w! \( c
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*, s" ]( T6 A/ I |% u3 y4 L
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* 4 w% K1 y- ^. V- t hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*% [( C+ a1 G4 a% U0 D
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa* 1 V Y6 k5 q7 h8 t4 {7 O cap)/((\[Gamma]a^\[Epsilon]*pa^(8 o) i, z" E. y, B. l/ Q
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*+ q- b4 |2 O7 X6 Z: O) O( \" v
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \ 4 S! \4 r4 x, T/ S) ^\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*! H/ l/ E* a' R) ?' b
xm (t)), , Q- m, x% n0 C. L
Sm[t] == (\[Gamma]m^\[Epsilon]* 8 Q) p+ R# H* q+ [ hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^( $ g- \. ]0 q' t, F0 F, ]- q$ g 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* 9 F3 `% g( u6 G! F- ? hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* 8 P- n: Q9 o/ ^3 j hs[t]^\[Theta]s)^(1 - \[Epsilon])), 8 D* |2 V/ k+ L8 [4 Q- \ Ss[t] == (\[Gamma]s^\[Epsilon]*(ps* ' e- i+ |2 Y; t2 R' Q hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(9 g. }( g4 R* g- b) K; y i
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*% P, }- A0 o' w) |, q
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* * j( y% o9 r+ M$ ]1 ]% W hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*; L5 C2 {( c+ ^, r& K
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps* ; K# j, @. M q% x9 Q csp)/((\[Gamma]a^\[Epsilon]*pa^(5 n) R* b6 M. D* a+ t/ x
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* * T5 F! `8 ?, U* _ hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \& F8 M; b* H3 z2 F, B/ _
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)* ) l. {1 A5 z; w+ ^) H5 h- c xm (t)), xm[0] == xm0, ) B4 O$ o, {6 v6 ?/ V xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, * Y6 C0 A& }1 a$ V7 i
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,; R, ^$ o' y B
0, TT}] ; o+ n1 a* n& F2 cPlot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], % P) a, _: v1 | Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, + M+ S) g6 p6 r- d$ `/ b4 w: D# a
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]! H1 j m& S. L' a$ j
Plot[{Evaluate[D*Sa[t] /. Sol], 6 S8 Y0 ~0 H& l" i Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 2 a/ x* E" Z* M% F gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, 3 u/ _% R4 R+ L$ {: Y$ S9 i B
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, 4 B3 P+ l- J0 m4 \. D
PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]8 C, D) b. Z* v
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5 k8 Y6 |, Q* Z8 C1 H! M
Set::wrsym: Symbol D is Protected. ; _; j' ?/ Z4 [$ l+ b F& u/ Y2 \0 y$ Y1 K6 v: 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.}./ Z' t3 T! p; c+ W( `0 I g
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7 k8 u( m6 M- Q1 U; Y$ q, n/ e: R 8 S% F7 E3 U# u; f( J, x