Hi I am a biologist and I want to model some ecological data that I have. I am new to mathematics and to ODEs. I want to write generic equations for a multi-dimensional system of ODEs. So, I want to look at "i" number of species(S) in "j" number of habitats and to study their population size as a function of time "t".
I have written generic mathematical equation for the system and it is given as: S'(i,j,t)= M(j-1) Ci S(i,j-1,t) - (Mj Ci + Dj) S(i,j,t);
where M - migration and depends on the habitat, C-chance of survival of individual species, D- death of the individual members of the species.
So, I can have i*j number of equations for this system and as an example the eqn for species-9 in the habitat-5 at time-10, would look like this:
S'(9,5,10)= M4 C9 S(9,4,10) - (M5 C9 + D5) S(9,5,10).
I want to write a generic equation in mathematica so that I can solve for very large number of i( say 100) in j=10 habitats, without writing the 1000 equations. Can I do this?
I want to have numerical or symbolic solution for this. But I don't know how to implement this in mathematica.