Stochastic patterns in a 1D Rock–Paper–Scissors model with mutation

In the framework of a 1D cyclic competition model, the Rock–Paper–Scissors model, where three kinds of generic agents are allowed to mutate, to interact and to move in space, we study the formation of stochastic patterns, where all the agents do coexist. We modelled the problem using an individual-based setting and we used the system size van Kampen expansion to deal with the Master Equation. We have hence been able to characterise the spatio-temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameter values beyond the ones fixed by the deterministic approach (mean field approximation). We complement such analytical results with numerical simulations based on the Gillespie algorithm.