dynamic generation of system of equations

Question

I am new to Mathematica and am trying to figure out how to dynamically generate a system of ODEs. For example I have a system of 100 equations where every 10 are essentially the same but with slightly different parameters that can be read from a vector (of length 10). I would like to write the 10 equations out, then loop over some iterator to generate all 100 equations. Is there a standard way to do this?

For example, here is a system of 30 equations (for i in 1:10):

 dX_i/dt = -\beta*X_i*Y_i + \delta_{i-1}*X_{i-1} - \delta_i*X_{i}
 dY_i/dt = \beta*X_i*Y_i - \gamma_i*Y_i + \delta_{i-1}*Y_{i-1} - \delta_i*Y_{i} 
 dZ_i/dt = \gamma_i*Y_i + \delta_{i-1}*Z_{i-1} - \delta_i*Z_{i} 

It seems redundant to copy paste new equations if I increase the i to say, 100 (i.e. giving us three hundred ODEs).

Answer 1

Here it goes, but probably Mathematica is not going to be able to solve it (depending on your coefficients)

Table[(delta[i] = i; gamma[i] = -i), {i, 0, 10}];
b = 1;
DSolve[Flatten@Table[{
    x[i]'[t] == -b x[i][t] y[i][t] + delta[i - 1] x[i - 1][t] - delta[i] x[i][t],
    y[i]'[t] == -b x[i][t] y[i][t] - gamma[i] y[i][t] + delta[i - 1] y[i - 1][t] - delta[i] y[i][t],
    z[i]'[t] ==  gamma[i] y[i][t] + delta[i - 1] z[i - 1][t] - delta[i] z[i][t]}, {i, 1, 10}], 
 Flatten[Table[{x[i][t], y[i][t], z[i][t]}, {i, 1, 10}]], t]