# Modeling a discrete probabilistic time evolution (in matlab?)

Good day, I am trying to model the following situation.

There is a system, which can be in three states. State M1, M2 and M3. From state M1, it can go into state 2 with probability p1. From state M2 it can go into state 1 with probability p2, and into state 3 with probability p3. From state M3 it can go into state 2 with probability p4.

Now my first attempt at tackling this was by working with a system of three coupled differential equations

$\dot{M_1} = -p_1M_1 + p_2M_2$

$\dot{M_2} = -(p_2+p_3)M_2 + p_1M_1+p_4M_3$

$\dot{M_3} = -p_4M_3 + p_3M_2$

But this doesn't really seem to work, as when I try to plot the solutions I'm not really seeing the expected dynamics.

So instead I want to try and solve it in a deterministic sense, but I honestly don't know where to begin. My guess is that one of the easier ways of doing so is by using matlab?

As for boundary conditions, I'd like to consider starting in M1.

Now I understand that I am really not giving you much, but I honestly don't have any idea where to begin. So my question basically boils down to how should I start tackling this problem, and is there any closely related problem that I can look up, to see how they handle that?

Kind regards

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You forgot to add what it is exactly you are trying to solve. –  AnonSubmitter85 Jan 15 at 12:10