Abstract
We propose a model to study the evolution of opinion under the influence of an external field on small world network. The macro-behaviour of agents' opinion and the relative change rate as time elapses are studied. The external field is found to play an important role in making the opinion s(t) balance or increase, and without the influence of the external field, the relative change rate γ(t) shows nonlinear increasing behaviour as time runs. What is more, this nonlinear increasing behaviour is independent of the initial condition, the strength of the external field and the time that we cancel the external field. The results may reflect some phenomena in our society, such as the function of the macro-control in China or the mass media in our society.