Abstract: Systems of non-linear ordinary differential equations can arise as the limit of a sequence of continuous time Markov chains. Even without passing to the limit, it is possible to write down companion ODEs and CTMCs that exhibit certain dynamical properties in common. For example, equilibria in an ODE model usually corresponds to a quasi stationary distribution (QSD) in the CTMC. Forward invariant subspaces of the phase space of the ODE correspond to closed communication classes in the CTMC. It also appears that ODE models which are point dissipative correspond to almost surely bounded Markov processes. In this talk, we will investigate dynamical features in CTMC models corresponding to bistability and periodic solutions in ODES models. These features can be hard to detect in CTMC models because the models usually lead to extinction in finite time. To over come this, we will modify the CTMC models to be ergodic and exploit properties of ergodicity to study the dynamics.