Last modified: 2014-03-28

#### Abstract

We study population dynamics using the generalized Rock-Paper-Scissors games with an arbitrary number of species. These models have proven to be a powerful tool in the study of the dynamics complex biological and ecological systems. We investigate the presence of string networks formed by the competition interaction between the species.We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator-prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. Using the field theory framework, we describe the dynamics of the network in terms of the density of empty sites. We perform and compare the results of a large number of stochastic Monte-Carlo-type numerical simulations and deterministic field theory ones by implementing the Lotka-Volterra equations. We find that the strings intercommute forming loops which collapse as in the cosmic strings networks in Cosmology. We also investigate models where the strings are formed by partneships formed when groups of species follow the maxim: the enemy of my enemy is my friend. The coexistence is achieved when the species form alliances which surround string competing regions. Finally, we compute the characteristic length and show that network evolves obeying the same scaling law of other curvature drive systems in nonlinear science.