Fixed points and maximal independent sets in AND-OR networks
Discrete Applied Mathematics
On limit cycles of monotone functions with symmetric connection graph
Theoretical Computer Science - Discrete applied problems, florilegium for E. Goles
Necessary conditions for multistationarity in discrete dynamical systems
Discrete Applied Mathematics
Positive circuits and maximal number of fixed points in discrete dynamical systems
Discrete Applied Mathematics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The singular power of the environment on stochastic nonlinear threshold Boolean automata networks
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
About non-monotony in Boolean automata networks
Theoretical Computer Science
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In line with fields of theoretical computer science and biology that study Boolean automata networks to model regulation networks, we present some results concerning the dynamics of networks whose underlying structures are oriented cycles, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits whose elements are updated in parallel. In particular, we give the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit. We also relate the counting of attractors of Boolean automata circuits to other known combinatorial problems and give intuition about how circuits interact by studying their dynamics when they intersect one another in one point.