Synchronization of drive–response singular Boolean networks |
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| Institution: | 1. Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China;2. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;3. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, P.R. China;1. School of Mathematics, Shandong University, Jinan 250100, Shandong, P. R. China;2. School of Management, Shandong University, Jinan 250100, Shandong, P. R. China;1. School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China;2. School of Mathematics, Southeast University, Nanjing 210096, China;3. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;1. School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;2. School of Management, Shandong University, Jinan, Shandong 250100, PR China |
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| Abstract: | Network synchronization, explicating typical collective behaviors of coupled systems, plays a crucial role in social production and life. This paper addresses the synchronization problem of drive–response singular Boolean networks (SBNs). The solvability of drive–response SBNs is investigated based on the matrix representation. In view of the existence and uniqueness of the solutions to drive–response SBNs, three types of concepts, synchronization, strong synchronization and weak synchronization, are put forward for the first time. By two new systems, a restricted BN and a switched restricted BN, which are constructed from the considered systems, several synchronization conditions are provided to deal with the circumstances of unique solutions and multiple solutions, respectively. Besides, the synchronous ratio is defined to characterize the synchronization capability of drive–response SBNs for the case of multiple solutions. Finally, several examples are given to illustrate the effectiveness of the obtained results. |
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| Keywords: | Cheng product Singular Boolean networks Solvability Synchronization |
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