Note: Comparison between parallel and serial dynamics of Boolean networks
Theoretical Computer Science
Positive circuits and maximal number of fixed points in discrete dynamical systems
Discrete Applied Mathematics
Discrete causal model view of biological networks
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
Singleton and 2-periodic attractors of sign-definite Boolean networks
Information Processing Letters
Static Analysis of Boolean Networks Based on Interaction Graphs: A Survey
Electronic Notes in Theoretical Computer Science (ENTCS)
Finding a Periodic Attractor of a Boolean Network
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points, depending on the architecture of the network.