I have an ODE system that increases in size according to the rules
n = 5;
T = 50;
nu = 0.05;
vars = Table[Subscript[x, j][t], {i, n}, {j, i}];
eqns = Table[{Subscript[x, j]'[t] ==
Subscript[x, j][
t] (1 - Subscript[x, j][t] -
nu (Sum[ Subscript[x, k][t] Boole[k != j], {k, i}]) ),
Subscript[x, j][0] ==
If[j == 1 && i == 1, 0.7,
If[j == i,
0.01 Subscript[x, RandomInteger[{1, j - 1}]][t] /. t -> T,
Subscript[x, j][t] /. t -> T]]}, {i, n}, {j, i}]
This codeI want solve the systemdifferential equation of accordingn variables, with interpolation structure
{{x1},{x1,x2},{x1,x2,x3},{x1,x2,x3,x4,},{x1,x2,x3,x4,x5}}initial conditions defined using the previous differential equation solution of n-1 variables and with an initial condition for the last variable (which randomly depends on one of the previous variables).
I'm having trouble building the initial conditions, present in the code above
Subscript[x, j][0] ==
If[j == 1 && i == 1, 0.7,
If[j == i,
0.01 Subscript[x, RandomInteger[{1, j - 1}]][t] /. t -> T,
Subscript[x, j][t] /. t -> T]]
Where the first initial condition {x1[0]=0.7}
The next {x1[0]=x1[Last time in j past],x2[0]=[Last time in j past]}
.
.
.
{{x1[0]=[Last time in j past],x2[0]=x2[Last time in j past],x3[0]==x3[Last time in j past],x4[0]=x4[Last time in j past],x5=0.01xSubscript[RandomInteger[1,j-1]][Last time in j past]}
can anybody help me?