Before revision:  The leading order term in these dynamical systems is called average dynamics and turns out to be an adequate concept to analyse such systemswith discrete and continuous state spaces. There are many complex systems that can be conveniently described inside such a state space setting, for example bio-molecular interactions. Both ODEs and Markov chains and their mutual interaction can be better understood and analysed through the  introduction of the so called Interaction Graph, a con- cept originally invented for time-continuous dynamical systems  [ 4 ].
After revision:  The leading order term in these dynamical systems is called average dynamics and turns out to be an adequate concept to analyse a class of simplified hybrid systems. Once the dynamics is defifined the mutual interaction of both ODEs and Markov chains and their mutual interaction can be better understood and analysed through the introduction of the so called Interaction Graph, a con- cept originally invented for time-continuous dynamical systems [ 4 ].