@article { , title = {Local negative circuits and cyclic attractors in Boolean networks with at most five components}, abstract = {We consider the following question on the relationship between the asymptotic behaviors of asynchronous dynamics of Boolean networks and their regulatory structures: Does the presence of a cyclic attractor imply the existence of a local negative circuit in the regulatory graph? When the number of model components n verifies n ≥ 6, the answer is known to be negative. We show that the question can be translated into a Boolean satisfiability problem on n · 2n variables. A Boolean formula expressing the absence of local negative circuits and a necessary condition for the existence of cyclic attractors is found to be unsatisfiable for n ≤ 5. In other words, for Boolean networks with up to 5 components, the presence of a cyclic attractor requires the existence of a local negative circuit.}, doi = {10.1137/18m1173988}, eissn = {1536-0040}, issn = {1536-0040}, issue = {1}, journal = {SIAM Journal on Applied Dynamical Systems}, note = {No embargo. OL 18.01.2019}, pages = {68-79}, publicationstatus = {Published}, publisher = {Society for Industrial and Applied Mathematics}, url = {https://nottingham-repository.worktribe.com/output/1481812}, volume = {18}, keyword = {Modelling and Simulation, Analysis}, year = {2019}, author = {Tonello, Elisa and Farcot, Etienne and Chaouiya, Claudine} }