Tonello, ElisaFarcot, EtienneChaouiya, Claudine2020-03-112020-03-112019-01-15Local Negative Circuits and Cyclic Attractors in Boolean Networks with at most Five Components Elisa Tonello, Etienne Farcot, and Claudine Chaouiya SIAM Journal on Applied Dynamical Systems 2019 18:1, 68-791536-0040http://hdl.handle.net/10400.7/932We 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 ∙ 2^n 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.engBoolean network, regulatory graph, local negative circuits, cyclic attractors, asynchronous dynamicsjournal article10.1137/18M1173988