Effects of inhomogeneous activity of players and noise on cooperation in spatial public goods games

We study the public goods game in the noisy case by considering the players with inhomogeneous activity of teaching on a square lattice. It is shown that the introduction of the inhomogeneous activity of teaching the players can remarkably promote cooperation. By investigating the effects of noise on cooperative behavior in detail, we find that the variation of cooperator density rhoC with the noise parameter kappa displays several different behaviors: rhoC monotonically increases (decreases) with kappa; rhoC first increases (decreases) with kappa and then it decreases (increases) monotonically after reaching its maximum (minimum) value, which depends on the amount of the multiplication factor r, on whether the system is homogeneous or inhomogeneous, and on whether the adopted updating is synchronous or asynchronous. These results imply that the noise plays an important and nontrivial role in the evolution of cooperation.