I am looking at a process with 2 distinct states, call them A and B. However, the number of the next state depends on the number of the current state, which can be chosen.
So for example, if $|A|_t$ = number of things in state A at time t, and $|B|_t$ = number of things in state B at time t, then in the next state ($t+1$), the state can be either:
$ |A|_{t+1} = |A|_t + |B|_t$, $|B|_{t+1} = |B|_t$
or
$ |A|_{t+1} = |A|_t$, $|B|_{t+1} = |A|_t + |B|_t$
Is there a name for this type of process? I know I have worked on Markov chains with bacteria models (theoretical) in stochastic processes courses, but I am trying to figure out if this would constitute a specific kind of Markov model (or if there is a name for it).
I just don't seem to remember the name of this type of process: I know there are birth-death processes, and perhaps some other stochastic processes with descriptive names that skip my mind at the moment.