Can a few fanatics influence the opinion of a large segment of a society?

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization and internet have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon, including: (1) There is a fundamental difference between a hierarchical network whereby people are influenced by those that are higher on the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually. (2) A few "fanatics" can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the "fanatics" disappear, the population may still remain susceptible to the positions advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population