Critical phenomena in rock-paper-scissors model

Abstract

This work presents a study on the dynamics of the Rock-Paper-Scissors (RPS) model, with particular emphasis on the influence of variations of the control parameters on the emergence and dissipation of spatial patterns as the system approaches a critical value. We observed that the model exhibits a continuous phase transition from the symmetric to the non-symmetric phase. We used the theoretical framework of critical phenomena as an analytical tool to explore the system stability in the vicinity of the critical point, allowing the calculation of the critical exponents. This research is important for a better understanding of the intricate behaviors and patterns observed in this type of system, and contributes significantly to the general field of complex systems research. Furthermore, this work established a link between the theory of critical phenomena and the dynamics of the RPS model, focusing on the emergence of critical behavior and the conditions that led to criticality and the characterization of the universality class. In summary, although it has been possible to obtain the critical exponents of the Rock-Paper-Scissors (RPS) model, the specific identification of its universality class remains unclear. This limitation results from the priority given in this thesis to the development of advanced methods capable of extracting significant information from the critical behavior of systems not directly related to thermodynamics. Nevertheless, obtaining the critical exponents is already an interesting achievement that emphasizes the unexplored potential of the RPS model. This model presents itself as a promising framework to address more complex questions in physics and biology, suggesting a vast field of possibilities for future investigations and applications.