Algebraic formulation and topological structure of Boolean networks with state-dependent delay

This paper investigates the algebraic formulation, topological structure and set stability of Boolean networks with state-dependent delay (SDD). Firstly, using the algebraic state space representation (ASSR) method, the dynamics of Boolean networks with SDD is converted into an equivalent augmented system. Secondly, based on the equivalent augmented system, some necessary and sufficient conditions are presented to calculate fixed points and cycles of Boolean networks with SDD. Thirdly, it is proved that the set stability of Boolean networks with SDD is equivalent to the set stability of augmented system, and a necessary and sufficient condition is presented by constructing a kind of set stability matrix. Finally, the obtained results are applied to the strategy consensus of networked evolutionary games with memories. (C) 2018 Elsevier B.V. All rights reserved.