Stabilization and oscillations design for a family of cyclic boolean networks via nodes connection

摘要

Boolean networks (BNs) are discrete-time logical systems, whose state evolutions are both determined by nodes' coupling connections and logical functions. This papers presents analytical studies on a family of cyclic BNs to achieve stabilization and oscillations via semi-tensor product (STP) method. The family of cyclic BNs shows a similar network structure (here we call nodes connection digraph), which is cyclic. Based on the cyclic network structure, a pinning control strategy imposed on any single node is proposed to achieve stabilization. Further, using model reduction method, the size of cyclic BNs is firstly reduced to a network with a single node, which preserves oscillations with the original network. Then, based on the reduced BN with single node, several sufficient conditions for oscillations are obtained, without using the traditional state transition matrix. Finally, the simulation of a network with 10 nodes is presented to show the efficiency of proposed method. (C) 2019 Elsevier B.V. All rights reserved.