Dynamics of semilattice networks with strongly connected dependency graph.
Automatica 2019 Jan; 99:167-174.
Discrete-time dynamical systems on a finite state space have been used to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being intuitive and the models can be easily simulated on a computer in most cases; however, few analytical tools beyond simulation are available. The motivation for this paper is to develop such tools. It identifies a broad class of discrete dynamical systems with a finite phase space for which one can derive strong results about their long-term dynamics in terms of properties of their dependency graphs. The paper contains a complete classification of the periodic orbits of semilattice networks with strongly connected dependency graph, by finding analytically the exact number of periodic orbits of any given period.
Veliz-Cuba, Alan and Laubenbacher, Reinhard, "Dynamics of semilattice networks with strongly connected dependency graph." (2019). Faculty Research 2019. 4.