Commun. Comput. Phys., 5 (2009), pp. 1045-1053. Continuous Opinion Dynamics in Complex Networks L. Guo 1, X. Cai 1*1 Complexity Science Center and Institute of Particle Physics, Huazhong (Central China) Normal University, Wuhan 430079, China. Received 12 July 2008; Accepted (in revised version) 3 September 2008 Available online 30 October 2008 Abstract Many realistic social networks share some universal characteristic properties, such as the small-world effects and the heterogeneous distribution of connectivity degree, which affect the dynamics in society system, especially the opinion dynamics in society. To see this, we study the opinion dynamics of the Improved Deffuant Model (IDM) in complex networks. When the two opinions differ by less than the confidence parameter $\epsilon$ ($0 < \epsilon < 1$), each opinion moves partly in the direction of the other with the convergence parameter $\mu$, which is a function of the opposite's degree $k$; otherwise, the two refuse to discuss and no opinion is changed. We analyze the evolution of the steady opinion $s_{*}$ as a function of the confidence parameter $\epsilon$, the relation between the minority steady opinion $s_{*}^{min}$ and the individual connectivity $k$, and find some interesting results that show the dependence of the opinion dynamics on the confidence parameter and on the system topology. This study provides a new perspective and tools to understand the effects of complex system topology on opinion dynamics. Notice: Undefined variable: ams in /var/www/html/issue/abstract/readabs.php on line 163 PACS: 05.45.-a, 87.23.Ge, 89.75.-k Key words: Opinion dynamics, complex networks, bifurcation phenomena. *Corresponding author. Email: longkuo0314@gmail.com (L. Guo), xcai@mail.ccnu.edu.cn (X. Cai)