Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \ " J$ h( ?3 w& Y\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]- ]5 J% t/ T g
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s = . w$ z6 I# h* B) n4 R/ o 1 - \[Gamma]a - \[Gamma]m; " J. x! D2 R y8 R+ _& s\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;. n) F+ t7 b( U. \
\[Theta]m = 0.75; \[Theta]s = 0.9;3 ~2 E% R8 `$ q4 Z# t3 p
gRate = 0.02;2 ?8 |7 Q# ]. G4 Q) o) i: w
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;( b$ k" O: `+ `- ?& @( R
ps = Bm/Bs; pa = Bm/Ba;$ w, ~4 |2 y1 N" J9 U- U8 V2 }# d6 l
\[Delta] = 0.03;. J/ D h# A' J W7 Q- j
B = \!\(TraditionalForm\`\* 4 w5 `+ k$ ]' Y$ W$ z+ Z5 |% E. FFractionBox[ 2 Z5 }! W1 Q1 L3 a- {0 @RowBox[{! M+ h. [7 k# j9 j A* ~
RowBox[{ 9 g `$ f8 J& t7 S) |RowBox[{6 A7 z7 W5 C( } a8 ^8 K }
StyleBox["(", ( v$ m. {! o! m3 Z0 y8 c6 f* r5 oSpanMinSize->1., ; ?: }' T0 b& Z4 C6 d4 n- ISpanMaxSize->1.], 1 ]! i5 U$ m' R( B) U' h$ p
RowBox[{"1", "\[Minus]", "\[Alpha]"}], / C2 F& i3 B: V. u
StyleBox[")",* c- d9 G: k7 H! ~4 }! C4 j' F
SpanMinSize->1.,( G n8 f9 `+ R' @4 i! w" Q
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}], $ [7 E" O9 J; U2 z* a$ a; C3 y
"\[Alpha]"] \[Minus] \[Delta]\);0 d* Q8 \$ P# a4 ~" K+ l5 u
cap = 10; S" H9 H( ?5 f. }$ _csp = (pa*cap)/ps;; U8 ^$ o S @5 k" y! |
D = ((1 \[Minus] \[Alpha])* " d" ~/ L; o1 l* b9 p gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);, C! T2 S, d( `2 G1 t
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1; & h5 w( j5 A$ v% A, U# W& gPrint["*** Initial Values ***"] " y$ a* T) p, K. nE0 = 1.5; : Y+ E3 V b5 V/ cK0 = E0/B; 4 O2 W7 ?5 e! h& [hm0 = 0.25; hs0 = 0.25;(* initial values *)6 ]6 r, s2 _; p1 d$ W
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;" a( {# t2 a4 s5 d/ f0 O! B
xm0 = (B*\[Gamma]m^\[Epsilon]*2 H1 [+ ?& w4 I( R# [1 h+ i$ _- }6 F# s
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(, _) ^5 v$ l0 k F2 k$ h; P
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* : z) ~5 H f8 [" T hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* + X& W$ Z8 l0 v) T, n# A5 p hs0^\[Theta]s)^(1 - \[Epsilon]));- Y/ \5 C8 `7 R6 {7 p: X2 i' u
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps* ) Z* {3 U5 X- k7 G hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^() Y5 Y8 T [; Q2 q
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* & [0 |/ U7 m8 ~4 X, N5 C hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*1 L8 G5 N( u* c7 B$ ^, ?
hs0^\[Theta]s)^(1 - \[Epsilon]));9 g T, I" y3 L) O2 f
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0], + c6 s# F" h z9 `$ i9 J
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0], 9 U: E4 t3 K/ R# Q6 W- ^2 _% F! l ", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]] / u( b+ e1 S; z6 K) I; ZTT = 100;(* end time *); Z, e1 C C: b& o& M
(* Solve differential equations *) 8 z; G8 Y4 H# l1 v- fSol = NDSolve[{xs'[t] = (1 - \[Epsilon])* ; w% O! B. x6 g$ i1 } xs[t]*( (1 - xs[t]/ 7 A, E4 q- }7 {* a; x. \6 [4 { B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) - 4 q0 S2 a1 H, ^6 A xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))), # C6 c9 m; N! ]% m _# L: U+ Q) g
xm'[t] == (1 - \[Epsilon])* % ?2 y# ]5 N' H& ] xm[t]*( (1 - xm[t]/ 1 c3 Z- y/ N4 S, p$ |( q B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) - 5 q* m( i0 |2 ?4 {; C( Z) u
xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1 t9 F( _0 l1 F2 k2 F A# }# p 1) ), \[Eta]m'[ ! h+ i$ V5 T" V t] == \[CurlyPhi]m* 8 |4 }: J) l* z. R' @! G* g xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[9 v$ T5 v6 |1 F. \4 I) T1 A
t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t], ' T% O- G/ P; T+ ~% R* p- K
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t], ' c2 S( T& h$ l, O( h hs[t] == \[Eta]s[t]*K[t], 1 C7 R+ a0 d) B
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\ ! e; m+ s7 M, J+ A\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*& Q0 y5 r; h+ q% K. Z! G
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* 0 l. n3 N6 p) o+ P1 {* @ hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]* % Y) V1 \. y& \( H hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa* s! y6 S) u4 q7 n( @0 p. D, p cap)/((\[Gamma]a^\[Epsilon]*pa^(, r3 K* B7 f' ?8 K1 r
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* 4 L Y; q4 `- e( x: \& A hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \$ t. a! [4 A( C2 `9 z
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)** U% d. L3 l+ M9 y1 S& z
xm (t)), + y( m( t% t, c' ? Sm[t] == (\[Gamma]m^\[Epsilon]** i0 n' ~1 u8 x% e' L# Z
hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(* \( m5 e) s! a
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*6 D, X3 S2 b* Q! T
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* K7 E8 Y% W8 x9 E/ W hs[t]^\[Theta]s)^(1 - \[Epsilon])), 9 t I9 y2 `' c& C! ~2 |, h
Ss[t] == (\[Gamma]s^\[Epsilon]*(ps* ; K0 Q4 U3 g+ z. X hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^( 4 ]; \' ]# g+ M: L 1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]* H. K( x# ~) `( K9 P; }3 h/ ] hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps* . d! S/ d2 r) J7 k3 i1 r# A hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]* # m( ?4 t& @6 T6 J% N hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps* 1 s. V( z2 ^( g- q$ j csp)/((\[Gamma]a^\[Epsilon]*pa^(; H" F, z% i; q2 ]$ p9 a8 u/ t9 d: C
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*( N# Q4 a) A, `& f& Z
hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \ 6 I$ a+ ` A/ c" x s\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)* ! f( ?: G+ ]; O$ M4 P xm (t)), xm[0] == xm0, 1 O8 w9 X, g0 M7 B* x
xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0, w. s, R n% r6 L
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t, " \/ b }* l% d; |1 U3 n 0, TT}]" X* H9 q! T2 ?' x8 s" b
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol], 9 f5 A0 @* p" R! \+ V Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0}, ( }9 `" ^: F F- ]
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]& T6 o: e2 U5 o* c( ?
Plot[{Evaluate[D*Sa[t] /. Sol], # H: [& y9 t+ Y" j+ p
Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] + 7 C* F# \4 G- r7 t! Z* S
gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT}, 6 o7 ?5 n1 m* @- X7 h2 `$ V* Y1 j4 L
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8}, 4 A: E, e, D1 |1 Y" `, [, { PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}] $ `$ k0 b1 [/ A + o/ \" i* f9 f+ x5 b9 o& P& i) N& U# D: \7 B6 |
! m# I2 q/ |6 T$ b9 P( W. I: C l `0 K8 f+ t4 e& S% Q( r) j" L
Set::wrsym: Symbol D is Protected. / p+ M" L6 |/ J : O' c. I% J2 ]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.}. ) A9 y/ N, [, x8 ~" M# K8 m1 v, g) ?