Competition and dual users in complex contagion processes

We study the competition of two spreading entities, for example innovations, in complex
contagion processes in random networks.
We develop an analytical framework and examine the role of dual users, i.e. agents using
both technologies. Identifying the spreading transition of the new innovation and the
extinction transition of a preexisting one, we find different phases depending on network
mean degree, prevalence of preexisting technology, and thresholds of the contagion processes.
Competition with the preexisting technology effectively suppresses the spread of the new
innovation, but it also allows for phases of coexistence. The existence of dual users
largely modifies the transient dynamics creating new phases that promote the spread of
a new innovation and extinction of a preexisting one. It enables the global spread
of the new innovation even if the old one has the first-mover advantage.