a=1.1;b=0.02;c=0.035;d=1.0;k=0.3;e=0.5;f=0.2;α=0.98;h=1;n=1+t;U[0]=0.3;V[0]=0.2;W[0]=0.5;
​
S
1
[t_]:=
(t-1)
α
α
((n+1)-(t+1))
-
(t+1)
α
α
((n+1)-(t+1))
-
1
α(α+1)
α-1
((n+1)-(t+1))
-
(t-1)
α
α
((n+1)-(t))
-
(t)
α
α
((n+1)-(t))
-
1
α(α+1)
α-1
((n+1)-(t))
;​​
S
2
[t_]:=
(t)
α
α
((n+1)-(t+1))
-
(t+1)
α
α
((n+1)-(t+1))
-
1
α(α+1)
α-1
((n+1)-(t+1))
+
1
α(α+1)
α-1
((n+1)-(t))
;
Ut=U[t]==U[0]+
1
Gamma[α]
(U[t]cd
a
(V[t])
-fcV[t]
a
(U[t])
)
h
S
1
[t]-
(b(U[t-1]cd
a
V[t-1]
-fcV[t-1]
a
(U[t-1])
))
h
S
2
[t];​​Vt=V[t]V[0]+
1
Gamma[α]
(cf(1-2V[t]-W[t])
a
(U[t])
+dc
a
(V[t])
U[t])
h
S
1
[t]-
(cf(1-2V[t-1]-W[t-1])
a
(U[t-1])
+dc
a
(V[t-1])
U[t-1])
h
S
2
[t];​​Wt=W[t]W[0]+
1
Gamma[α]
(df(1-V[t]-W[t])
a
(U[t])
)
h
S
1
[t]-
(df(1-V[t-1]-W[t-1])
a
(U[t-1])
)
h
S
2
[t];​​
{Us,Vs,Ws}={U0,V0,W0};
Do[{Us,Vs,Ws}={U[t],V[t],W[t]}/.Last[NSolve[{Ut,Vt,Wt}/.Thread[{U[t-1],V[t-1],W[t-1]}{Us,Vs,Ws}],{U[t],V[t],W[t]}]];​​sol[t]={Us,Vs,Ws};​​,{t,1,10}]
Table[sol[i],{i,1,100}]
​