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Emergence of Global Leader-Follower Structure via Local Social Interactions
Most mathematical models of influence processes in social groups focus on how the underlying social network structure shapes the opinion evolution. This project studies the opposite direction: how certain network structures emerge from opinion exchanges.
Keywords: social networks, nonlinear systems
Opinion dynamics is an area of applied mathematics that studies the modeling and analysis of how individuals in social groups influence each other's opinions, and what macroscopic patterns emerges from the local interpersonal influences. Most mathematical models of opinion dynamics assume that the interpersonal influence network is predetermined, either fixed or time-varying. The leader-follower relations play a crucial role in determining the behavior of opinion dynamics. However, few models studies where such leader-follower structure comes from. This project proposes and analyzes a novel model that explains the emergence of certain sophisticated leader-follower structure, via the coevolution between interpersonal appraisals and influences.
Opinion dynamics is an area of applied mathematics that studies the modeling and analysis of how individuals in social groups influence each other's opinions, and what macroscopic patterns emerges from the local interpersonal influences. Most mathematical models of opinion dynamics assume that the interpersonal influence network is predetermined, either fixed or time-varying. The leader-follower relations play a crucial role in determining the behavior of opinion dynamics. However, few models studies where such leader-follower structure comes from. This project proposes and analyzes a novel model that explains the emergence of certain sophisticated leader-follower structure, via the coevolution between interpersonal appraisals and influences.
The student will first get familiar with the mathematical tools frequently used in opinion dynamics. Then she/he will characterize the set of equilibria and establish the convergence of the new model. If possible, the student will further investigate other important dynamical behavior of the new model.
The student will first get familiar with the mathematical tools frequently used in opinion dynamics. Then she/he will characterize the set of equilibria and establish the convergence of the new model. If possible, the student will further investigate other important dynamical behavior of the new model.