Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \ + E* M) M( c# ~\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]], R9 q6 ~2 x; [7 ~
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = 5 |2 t9 L0 }2 v: b
1 - \[Gamma]a - \[Gamma]m; 4 N+ X i1 n( i* p7 B, y0 n\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;+ `" p* l z& S4 K
\[Theta]m = 0.75; \[Theta]s = 0.9; ; h# M2 I3 B( d+ K; VgRate = 0.02; . c8 q8 b% h& m7 [Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;, w1 P! ^. ]: U* Z- i5 w
ps = Bm/Bs; pa = Bm/Ba;' L) G8 m% l' X+ t$ N
\[Delta] = 0.03;+ ~" U3 g3 L* D0 D- s: k L3 R6 f
B = \!\(TraditionalForm\`\* ! ^0 {% e! S# Z0 ~( ]7 SFractionBox[0 C5 d) S1 g' F4 ]
RowBox[{ 3 o" {- F* m; H9 W2 H. g+ F: ?4 RRowBox[{ , m8 m& v/ I5 R* D6 T6 _RowBox[{ 8 m8 o5 l- u' `# ]2 } }. mStyleBox["(",9 R' N( h( N) G, o/ Z3 c
SpanMinSize->1., . L- N* j( Y" {2 m. W. N3 h' BSpanMaxSize->1.], . q+ ^7 Y+ k6 o
RowBox[{"1", "\[Minus]", "\[Alpha]"}], 4 W6 q& S1 g; S4 A& Q' |) Z
StyleBox[")"," M% f6 J8 I$ o' O, O! X
SpanMinSize->1.,3 O- q9 x* E' T7 T+ B
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], 0 e! b( M9 G5 Q( y ` "\[Alpha]"] \[Minus] \[Delta]\);8 a) t' S8 ~9 h& n
cap = 10;* S) x; X; T; @5 B& D$ |2 b8 r
csp = (pa*cap)/ps; ( G7 B2 Z5 D+ s0 s) rD = ((1 \[Minus] \[Alpha])* 3 ]) b- `! S s, m& _- O* C$ a gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);5 o8 X# y( R% ~0 n1 Z# d" v8 [
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;0 P: W) p. Z- l9 b' ?7 w( I
Print["*** Initial Values ***"] ; k3 s4 V# ?% a4 U2 zE0 = 1.5; & J- ^8 C; M, i9 c& aK0 = E0/B; , B- R3 p: O& A5 H; }3 v; W9 ^hm0 = 0.25; hs0 = 0.25;(* initial values *) 4 ^# a5 v4 U( X& h: S/ m\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0; v+ a) t8 n4 n. ^xm0 = (B*\[Gamma]m^\[Epsilon]* 9 G% A2 C( N# g, J+ F hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^( ! n, \# L; d$ @3 b 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*0 l3 p: s6 X" a+ Z* W# E7 C, O0 e
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* ( n! D* q. W( c$ `' Y# D hs0^\[Theta]s)^(1 - \[Epsilon])); 8 Q ]" U0 D0 A' vxs0 = (B*\[Gamma]s^\[Epsilon]*(ps* 5 @! `) @ O. N" I hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^( . l* R a @7 u- P 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* / i3 v9 k* ?2 F5 e5 T: z: v hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* ) n( R0 O+ L% t2 y, f2 h hs0^\[Theta]s)^(1 - \[Epsilon])); 1 Z+ i0 x8 c' O7 T7 nPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], " h; x5 O4 y. I8 A& @6 i ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], : j' y$ Q, R. W9 v9 x
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]) @8 {7 D; _- |; T, @2 T ^. i
TT = 100;(* end time *)/ l: A4 [5 ~& p' I& P
(* Solve differential equations *) 5 N C" v! K0 B# G/ c# U( {2 O# sSol = NDSolve[{xs'[t] = (1 - \[Epsilon])* 2 _* }* V0 _2 ?5 T5 S5 o# f, T xs[t]*( (1 - xs[t]/, G# k$ t h' h: `% A$ }. |8 i
B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - % f6 q, V5 i. v xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), 7 Q$ a2 ^4 A% \$ m! _ xm'[t] == (1 - \[Epsilon])*9 @" {: O6 j6 d& c/ ~
xm[t]*( (1 - xm[t]/2 o R" ~8 H; b# H! Z# m
B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - - T8 d! P+ j7 t2 U
xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 7 G; ?1 y% k+ Q; x A8 @$ f5 w( j0 |! |* D
1) ), \[Eta]m'[! y" x3 b! s: F+ \
t] == \[CurlyPhi]m* 5 q5 t" \2 C m9 }' e xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[ 6 Q; a1 N* R; y& |7 ]# O7 U& } t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], ) d& o" j# t P8 y4 r8 E; G
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], % k; w" Q* \6 b2 o* \
hs[t] == \[Eta]s[t]*K[t], 5 y' [8 v5 d1 G# {# s
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\ 3 D/ P# w! w8 S1 B5 s8 Q; I6 ^\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*" }- e T! {- J% l& @7 o
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*2 L! h- a9 @1 |+ E6 C8 O k; q
hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*4 W. z5 H V$ U( t
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*% l! l+ A' L3 `# N; ^
cap)/((\[Gamma]a^\[Epsilon]*pa^( / @" ?" l' j8 I* g' t$ X* u5 L5 q 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* ; K! G& h" [" a& ^ F hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \+ L4 l9 i, K, T6 G+ Z
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*" ?, f/ D* _$ t) D
xm (t)), " U9 I- ] n& i
Sm[t] == (\[Gamma]m^\[Epsilon]* 9 L0 {, ~5 }) i: ?+ T5 u8 u hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^( 5 p) S5 f# ~% l7 _2 B2 z) P7 R' g 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* 0 f7 c! j6 j; c hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* : O: Y9 {, v# m: v* f5 u2 O hs[t]^\[Theta]s)^(1 - \[Epsilon])), % {3 j2 E* Y3 ~8 x Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*& \! W; Z2 C+ g( f3 M' V
hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^( & P0 V# s6 R _9 n# j 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* 5 w" R& b9 j2 l( U/ f! k hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* 5 u2 T# F: A) \ F' k, K hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*( u# ?: j! b& l8 c
hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps* 5 k' g2 J+ }$ w) T' N4 X csp)/((\[Gamma]a^\[Epsilon]*pa^(4 L1 o+ T) M3 x" Z2 N3 H
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* & G/ S5 \ q6 c% f7 `& } hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \. S( t! @, N. G3 O( h4 c) p
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*3 \8 ^8 l6 {# Z
xm (t)), xm[0] == xm0, 6 r% a+ Z5 j$ b$ g5 i xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, ; N4 @0 O. E- P" O) o3 c K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,. y7 N# q: \. M0 z) b8 x3 ]5 s4 C
0, TT}] 7 E/ v3 u8 g i1 [0 T; LPlot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], ) @: N8 H8 y8 |6 `, Z/ c Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, { w3 P. s: `! A/ J+ q6 Z PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]- |9 s) w0 y) k
Plot[{Evaluate[D*Sa[t] /. Sol], 8 ~2 S1 C# v% N
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + % X/ K/ g) e2 p gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, $ T* a- Y6 s) D" V. Q AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, 8 G6 ~; D- T1 O7 \ PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]* m5 ~* d' m: H; X. v6 g2 p
1 ~% ~5 y& y) J; \) _) n( h6 U
: `7 O* u3 x0 {; A! K# ^9 F: l4 B. Q7 @& N0 U1 I
2 C, \" f. \. L) W& G1 l2 k1 lSet::wrsym: Symbol D is Protected. 6 r( Y2 ]$ X! I( |; i' C; N$ _1 G. v! N; v& a) H/ W3 e. J
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.}. & p5 P. ?. u2 Z+ G" n- B; i4 r- T# V4 s
0 t+ s, d' T& b2 H7 b
0 ]. l; H I, b7 {% N; ]3 {: l d
4 G0 F4 [8 v$ R. D9 [