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Global Stability of Social Networks
Date: 2017/12/21             Browse: 39

Speaker:     Assistant Prof. Ji Liu.  SBU

Time:          Dec   21.     15:00   —   16:00 

Location:    Room 1A-200, SIST Building

Host:          Prof. Jie Lu


The talk will focus on global stability of two discrete-time models for opinion dynamics in social networks. The first part will consider the discrete-time version of Altafini’s model for opinion dynamics in which the interaction among a group of individuals is described by a time-varying signed digraph. Exponential convergence of the system will be established using a graphical approach. Necessary and sufficient conditions for exponential convergence with respect to each possible type of limit states will be provided. Specifically, under the assumption of repeatedly jointly strong connectivity, it will be shown that (1) a certain type of two-clustering can be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced. The second part will address a study of the opinion dynamics that emerge in a scenario where individuals consecutively discuss a sequence of issues. Specifically, we will discuss how individuals’ self-confidence levels evolve via a reflected appraisal mechanism. Motivated by the DeGroot-Friedkin model, we will introduce a Modified DeGroot-Friedkin (MDGF) model, which allows individuals to update their self-confidence levels by interacting with only their neighbors. In particular, the modified model allows the update of self-confidence levels to take place in finite time without waiting for the opinion process to reach consensus on any particular issue. For the case when the interaction matrix is doubly stochastic, we will show that for the MDGF model, the vector of individuals’ self-confidence levels converges to a unique nontrivial equilibrium, which for each individual is equal to 1/n, where n is the number of individuals. This implies that eventually individuals reach a democratic state.


Ji Liu received the B.S. degree in information engineering from Shanghai Jiao Tong University, Shanghai, China, in 2006, and the Ph.D. degree in electrical engineering from Yale University, New Haven, CT, USA, in 2013. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering at Stony Brook University, Stony Brook, NY, USA. Prior to joining Stony Brook University, he was a Postdoctoral Research Associate at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA, and the School of Electrical, Computer and Energy Engineering at Arizona State University, Tempe, AZ, USA.

His current research interests include distributed control and computation, multi-agent systems, social networks, epidemic networks, and power networks.

SIST-Seminar 17069