Abstract—Consensus problems of an opinion dynamical system without a leader and with a leader under CS and MT influence functions are studied and a simple proof to guarantee that an opinion dynamical system can reach a consensus is also obtained in this paper. Moreover, results show that the system with a leader reaches a consensus more slowly than that without a leader by numerical simulations.

Index Terms—Dini derivative, Lyapunov function, opinion consensus.

The authors are with College of Science, National University of Defense Technology, Changsha, Hunan, P. R. China (email: wxiao_98@nudt.edu.cn).

Cite: Ye Cheng, Xiao Wang, Xiongwei Liu, "Asymptotic Behaviors of an Opinion Dynamical System without or with a Leader," International Journal of Applied Physics and Mathematics vol. 6, no. 3, pp. 80-87, 2016.