Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems

Details Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems

2011-03-15

arxiv.org/abs/1103.2829v2

Mathematics

Dynamical Systems

22 pages, Submitted to SIAM Journal on Control and Optimization (SICON)

Scientific paper

Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of each agent can be defined as either (1) those agents whose opinions are in its "confidence range," or (2) those agents whose "influence range" contain the agent's opinion. The former definition is employed in Hegselmann and Krause's bounded confidence model, and the latter is novel here. As the confidence and influence ranges are distinct for each agent, the heterogeneous state-dependent interconnection topology leads to a poorly-understood complex dynamic behavior. In both models, we classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. Then, we define a positive invariant set centered at each equilibrium opinion vector. We show that if a trajectory enters one such set, then it converges to a steady state with constant interconnection topology. This result gives us a novel sufficient condition for both models to establish convergence, and is consistent with our conjecture that all trajectories of the bounded confidence and influence models eventually converge to a steady state under fixed topology.

Affiliated with

Also associated with

No associations

Rating

Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-138415