I'm not sure if I'm using the correct nomenclature, but I wish to model a hypothetical biological system. I have a basic knowledge of discrete-time Markov chains, so let me explain the problem as best I can.
Suppose I have a system with two actors, A and B. Each actor, is capable of performing an action at a specific (continuous) rate. Let's assume the rate at which A and B perform work, each follow a Poisson distribution.
Actor A's work rate has a positive feedback effect on A, and inhibitory effect on B. Similarly, actor B's work rate inhibits A, but has a negative feedback effect on B.
A <--- A --X--> B
B <--X-- B --X--> A