Speaker: Zhang Xiao received his B.E. and Ph.D. degrees from Shandong University, Jinan, Shandong, China, in 2015 and 2020, respectively. During 2018-2019, he was a visiting researcher at the University of Texas at Arlington, Arlington, TX, USA. During 2020-2023, he worked with the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, as a special research assistant. Currently, he is a postdoctoral fellow at the Department of Applied Mathematics, Polytechnic University of Hong Kong, Hong Kong SAR， China. His research interests include game theory， Boolean networks, and game theoretic control.

Date: November 26, 2023

Time: 10:00-12:00

Location: Tencent Meeting: 346 586 616

Sponsor: School of Mathematics, Shandong University

Abstract:

It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using the semi-tensor product (STP) of matrices and the algebraic state-space representation (ASSR) of Boolean networks, this paper reveals that in addition to this explicit order, there is a certain implicit or hidden order, which is determined by the fixed points and limit cycles of their dual networks. The structure and certain properties of dual networks are investigated. Instead of a trajectory, which describes the evolution of a state, the hidden order provides a global horizon to describe the evolution of the overall network. We conjecture that the order of networks is mainly determined by the dual attractors via their corresponding hidden orders. Then these results about Boolean networks are further extended to the $k$-valued case.

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https://www.view.sdu.edu.cn/info/1020/185703.htm