Applications of quadratic stochastic operators to nonlinear consensus problems

Historically, the idea of reaching consensus through repeated averaging was introduced by De Groot for a structured time-invariant and synchronous environment. Since that time, the consensus, which is the most ubiquitous phenomenon of multi-agent systems, becomes popular in the various scientific fields such as biology, physics, control engineering and social science. In this paper, we give an overview of the recent development of applications of quadratic stochastic operators to nonlinear consensus problems. We also present some refinement and improvement of the previous results.