Skip to Main content Skip to Navigation
Conference papers

Effect of Graph Structure on the Limit Sets of Threshold Dynamical Systems

Abstract : We study the attractor structure of standard block-sequential threshold dynamical systems. In a block-sequential update, the vertex set of the graph is partitioned into blocks, and the blocks are updated sequentially while the vertices within each block are updated in parallel. There are several notable previous results concerning the two extreme cases of block-sequential update: (i) sequential and (ii) parallel. While parallel threshold systems can have limit cycles of length at most two, sequential systems can have only fixed points. However, Goles and Montealegre [5] showed the existence of block-sequential threshold systems that have arbitrarily long limit cycles. Motivated by this result, we study how the underlying graph structure influences the limit cycle structure of block-sequential systems. We derive a sufficient condition on the graph structure so that the system has only fixed points as limit cycles. We also identify several well-known graph families that satisfy this condition.
Document type :
Conference papers
Complete list of metadata
Contributor : Hal Ifip Connect in order to contact the contributor
Submitted on : Friday, January 20, 2017 - 4:09:40 PM
Last modification on : Monday, January 23, 2017 - 2:10:50 PM
Long-term archiving on: : Friday, April 21, 2017 - 3:51:22 PM


Files produced by the author(s)


Distributed under a Creative Commons Attribution 4.0 International License



Abhijin Adiga, Chris J. Kuhlman, Henning S. Mortveit, Sichao Wu. Effect of Graph Structure on the Limit Sets of Threshold Dynamical Systems. 21st Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2015, Turku, Finland. pp.59-70, ⟨10.1007/978-3-662-47221-7_5⟩. ⟨hal-01442482⟩



Record views


Files downloads