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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \2 b2 N9 L; J% J( C
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
; L+ a. c- h# g) Z4 _: X0 G) o/ ^2 [9 x\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = ; H; W* `( b# l& F& }
1 - \[Gamma]a - \[Gamma]m;
$ @3 p3 G8 l: F\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
/ B: g$ G/ U: I- L5 j\[Theta]m = 0.75; \[Theta]s = 0.9;' p9 y/ w+ ?7 `% a$ B v+ E) Q
gRate = 0.02;* G% c" L" r1 n; q( b5 ]. V" |7 I
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
/ n* n, l E1 J9 P3 \- H, L5 ]ps = Bm/Bs; pa = Bm/Ba;# m6 D- q+ p v3 |0 D9 y
\[Delta] = 0.03;
) j6 @/ z e$ bB = \!\(TraditionalForm\`\*8 U' d3 t3 }$ C/ }+ R% I0 N# j
FractionBox[4 H! R8 C* |4 u, h& g
RowBox[{5 @8 ^( t, j+ R1 q+ K6 A: f$ {
RowBox[{
6 s7 A& F/ f d) U& M \RowBox[{* ]% O& _, u0 t8 m3 g" D5 Z! p7 J
StyleBox["(",
: G5 Q {8 i7 B8 c5 `0 V0 `. wSpanMinSize->1.,
# G% R _4 Y) @: {" wSpanMaxSize->1.],
( |$ V l! z' X" BRowBox[{"1", "\[Minus]", "\[Alpha]"}], : G( K& |3 G& g) Q
StyleBox[")",
( E: b' p7 b- M$ J% w; nSpanMinSize->1.,0 {' |/ i7 a j1 I" y' B
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], * z8 l3 p8 r6 [7 U
"\[Alpha]"] \[Minus] \[Delta]\);
" e8 `2 k' J+ G( Lcap = 10;
/ I* F G2 g4 Rcsp = (pa*cap)/ps;
2 Z2 G/ h- ^; g- u1 uD = ((1 \[Minus] \[Alpha])*/ P6 H, O+ I/ A- D' I
gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
1 B3 J/ N2 v6 n- p\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;' k6 q V" p) l' c r
Print["*** Initial Values ***"]
! N5 } }1 G4 g9 LE0 = 1.5;
# d( v, z1 s3 |5 z* H" gK0 = E0/B;/ K) T" _& x& h3 k% T, T9 r
hm0 = 0.25; hs0 = 0.25;(* initial values *)
R1 _6 g2 Q7 ]% k+ a- K+ U! ]+ x\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
b. M. o2 z& R) Q0 @) s1 @4 yxm0 = (B*\[Gamma]m^\[Epsilon]*: j" W2 ?7 a. Y4 k; m
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
, `# w* T& f. X6 T+ h' T! ^ 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
5 X- c: b6 A7 G& y$ a+ r# g hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*1 I; X+ M" |* x8 {
hs0^\[Theta]s)^(1 - \[Epsilon]));& t) S% V7 g$ }1 z, n
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
0 t) S1 y( E: q- J, _ hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(" y! b% V5 y' d
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*; W1 U$ F% i, Q% L
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
; _$ Y& F3 e9 ^ f& K hs0^\[Theta]s)^(1 - \[Epsilon]));$ F7 ^& h" ^7 x/ ^' L! |
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
5 n" {, M' a1 c n! J1 m ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], # `% A2 l7 E6 {( `% z- q9 l
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
( l' P B3 P5 S( \TT = 100;(* end time *)& v1 g/ o( C, J
(* Solve differential equations *)
& r' I' H- N% ~4 N0 j/ qSol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
& x8 W8 y5 ]* ^% }+ G) c2 y; [ xs[t]*( (1 - xs[t]/
- s0 `' m8 X" X5 b( @; v# ]& U9 X B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - * U( K- R, l$ e2 I2 E& {! s
xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
0 f, h4 q- `/ W. l" h+ W* A xm'[t] == (1 - \[Epsilon])*
6 T! X/ a( `3 e7 @ xm[t]*( (1 - xm[t]/
: j [8 F N: S1 O& ^; Q. s% i B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
- S$ P; P% p( l }1 U" r5 b xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
( d, W5 N" ?; O3 Y2 X 1) ), \[Eta]m'[
+ b# X- Q- c" y, W! U3 p( f e. T t] == \[CurlyPhi]m*) W4 P5 t( G/ @* A% z/ f4 M
xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[$ ]- J0 I h/ S& ^! p
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
$ z3 m) p& E+ g K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
. p: \( W# Z+ t, w hs[t] == \[Eta]s[t]*K[t],
# k. P/ T/ A& G5 _" e! n1 d! B; H Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\2 c( {+ R3 b" t. J$ Q
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
. x! q! B' `- ]4 K/ ^% y; g; v hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
8 x, B1 p, p: a$ b4 F# e hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*1 R3 ~* C6 b- i: ^6 b
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*5 Q' {4 j0 L. e2 G# ~
cap)/((\[Gamma]a^\[Epsilon]*pa^(* G- `0 |" A+ @) I; P& `& P+ X; _
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
' m# V$ `+ s; Y& Z8 s hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \4 D& q s% K4 U: L3 }
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
) ^1 }; S2 i/ ] b4 B( F2 n# u% Y xm (t)), & B6 O0 x3 B- d- T' Y0 z) X% s
Sm[t] == (\[Gamma]m^\[Epsilon]*. h" M. f6 ^- P# [4 ~
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
$ t* g- H% G4 }: J# I 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" P! k2 [# w; G
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*5 s' o! u7 e+ G# j7 R1 t& I- e
hs[t]^\[Theta]s)^(1 - \[Epsilon])),
! ~; E7 B" S$ }) Y Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
3 a+ G" p4 C9 o4 |+ o hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(9 `1 d$ ]2 N4 a4 J8 {
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
; p% } t$ N7 L+ N$ l% o6 H hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*/ y) y) |/ s0 K: {7 O i3 T: y% t* q8 k
hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*% K2 {9 v1 J# ?8 f- K% G
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*8 x/ p1 z) J. Q0 Z
csp)/((\[Gamma]a^\[Epsilon]*pa^(' i) A5 g! z, g9 _1 c
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*% _1 f1 ?! V7 ~
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
: {" p5 L/ B1 j7 M* |( p* e% a\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
* T F0 k" Q* D! b# N2 T4 b2 d xm (t)), xm[0] == xm0, + D7 w- {3 \: }) c/ Y
xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
: ]: _; E" V% _, a- X3 V9 j K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,/ ^0 D* i! Q% z& Q; f( g+ U2 X
0, TT}]
! E: q" N8 h4 ^Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], 9 q8 a6 o$ ^4 ~* _, B/ R
Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
% ^0 G8 T/ _. r" C/ ]6 C5 \ PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]6 Y7 W; J7 W5 k
Plot[{Evaluate[D*Sa[t] /. Sol], , M, h; r5 z: p6 G
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 1 `* v9 T+ O U8 `' m: D( @7 S
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
0 A- D2 P1 t( O/ L/ ? AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, / E/ e* t' q8 b; i
PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
7 L3 v- b$ u: a8 G" R9 W0 S% k. o" r7 r7 C# O# J
9 z) C0 h! C/ t6 @, k
+ [4 b2 E0 H H( X) c# |! S
. m$ {, R7 O/ M2 a8 I
Set::wrsym: Symbol D is Protected., f N; `8 d a. W. F6 S
! l4 M: P! Y" u* k
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.}.
! W* n" n7 _. F6 P0 w+ T
u) U3 w. ~$ Q; Q1 K" M9 h z0 h* L" |. r! S y& S6 H% c
0 f; P3 q& u3 _5 S
0 E4 D3 r# P4 L% O9 w6 l1 y r
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