2010/10/02 by Alan Veliz-Cuba, Alan Veliz‐Cuba, Reinhard Laubenbacher +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Gene Regulatory Network Analysis #Microtubule and mitosis dynamics #math.CO
paper · pdf · doi:10.48550/arxiv.1010.0359
9 pages, 2 figures
arxiv created 2010/10/02 · openalex publication_date 2010/10/02 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being intuitive and 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 for the analysis of models in biology. In this paper we have identified 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. We classify completely the limit cycles of semilattice networks with strongly connected dependency graph and provide polynomial upper and lower bounds in the general case.