Critical phenomena in the Rock-Paper-Scissors model

This work studies the dynamics of the Rock-Paper-Scissors (RPS) model with May-Leonard dynamics, with particular emphasis on how variations in control parameters affect the emergence and dissipation of spatial patterns as the system approaches the critical point. We observed that the model undergoes a phase transition from a symmetric to a non-symmetric phase. We applied the theoretical framework of critical phenomena to analyze the stability of the system near the critical point and calculated the critical exponents. This approach brings a new way to find critical mobility, which can jeopardize biodiversity. Our understanding of the complex behaviors and patterns inherent in such systems contributes to the general field of complex systems research which can be improved by this research. Moreover, this work bridges the theory of critical phenomena with the dynamics of the RPS model, identifying conditions leading to critical behavior, and contributes to the characterization of its universality class.