Criticality in evolutionary games

The criticality of a dynamical system is extremely significant for evolutionary networks. The term criticality, which originates from statistical physics, implies that the system is extremely susceptible to small perturbations, and is closely related to the concept of a tipping point from Deliverable 2.2. Moreover, a critical system obeys certain scaling laws. In systems with many components such a regime can be detected from the spectrum of the evolution operator, that governs the dynamical system. It has been suggested by Kaufman that living systems should be near a critical state in order for Darwinian evolution to be successful. In fact the total system self-organizes such that it is poised at the edge of chaos. The mathematical aspects of how systems in evolutionary game theory actually evolve toward criticality is a challenge for which we will turn to Lyapunov exponents for large networked systems with adaptive dynamics for their topology. The analysis requires both analytical methods and numerical simulations.