Stylistic evolution in networks: delayed dynamics in style emergence

Abstract

We simulate the evolution of styles in a system of interacting agents. Our motivation is to study the emergence of popular music genres such as tango or jazz. In our model, style is represented by a real number in the range 0–10. We assume that given a network of interacting agents, each agent assimilates features from their neighbors’ styles. We will say that two agents are neighbors when their styles are similar (numerically close to each other). Observe that the network structure itself evolves as the agent styles change. The interplay between musicians in the Americas in the second half of the XIX century was strongly dependent on their physical interaction, due to the lack of sheet music and recording devices, specially among non-reading musicians. We focus in a crucial aspect of interaction, a temporal delay. This delay arises when musicians playing together assimilate features not just of the present style of the others but also of their past style or their tradition; delay can be also caused by slow speed of information transmission, or due to technological limitations. The style of each agent is initialized by a real number in the range 0–10 assigned randomly with uniform distribution. The values of the agents are allowed to evolve randomly and independently during a certain time before the beginning of interactions. After that lapse, their evolution is similar to opinion dynamics models, where each agent replaces its own style with some weighted average of the styles of their neighbors. Numerical simulations show the effects of the delay, which produces slower convergence to more different styles (several clusters of fully connected agents) in comparison with non delayed interactions, in which only the present styles of agents have influence and not their past. Moreover, we consider the effect of heterophily (when the intensity of interaction is greater for agents that are dissimilar in style) and of popularity, where a second evolving network, simulating the public, establishes a ranking of the agents according to how much public is in their neighborhood; the rank of an agent determines the strength and the extent of its influence.