Nonautonomous dynamical systems help us to understand the implications of real which are in contact with their environment as it actually occurs nature. Here, we focus on where a parameter changes time at small but non-negligible rates before settling stable value, by using Lorenz system for illustration. This kind commonly show long-term transient dynamics previous sudden transition steady sta...

We analyze the dynamics of agent–based models (ABMs) from a Markovian perspective and derive explicit statements about the possibility of linking a microscopic agent model to the dynamical processes of macroscopic observables that are useful for a precise understanding of the model dynamics. In this way the dynamics of collective variables may be studied, and a description of macro dynamics as ...