  Individuals accepting an idea may intentionally or unintentionally impose
influences in a certain neighborhood area, making other individuals within the
area less likely or even impossible to accept other competing ideas. Depending
on whether such influences strictly prohibit neighborhood individuals from
accepting other ideas or not, we classify them into exclusive and non-exclusive
influences, respectively. Our study reveals for the first time the rich and
complex dynamics of two competing ideas with neighborhood influences in
scale-free social networks: depending on whether they have exclusive or
non-exclusive influences, the final state varies from multiple coexistence to
founder control to exclusion, with different sizes of population accepting each
of the ideas respectively. Such results provide insights helpful for better
understanding the spread (and the control of spread) of ideas in human society.
