Chaotic Synchronization And Public Goods Games In Small-World Networks

In this paper, the enhancement of the synchronizability of the networks is analyzed when the time-dependent coupling strengths are coupled to the dynamics of the nodes in small-world networks. The effects of noise and inhomogeneous activity of nodes in public goods games on small-world networks are discussed.Firstly, to enhance the synchronizability of small-world networks, the relation of the time-varying rate of the coupling strength between connected nodes and the dynamics of the two nodes is analyzed. From the time-varying couplings, it is found that the changes of mean coupling strength and the time taken for the transition of network dynamical systems from uncorrelated state to global synchronization in time-varying coupling are much smaller than that in fixed-coupling strength when the shortcut numbers are different.Secondly, the public goods games in small-world networks are discussed. The effects of noise and inhomogeneous activity of nodes is analyzed. It is found that the effects of small-world character and noise can reduce the emergences of cooperators. While the inhomogeneous activity of nodes can enhance the emergences of the cooperative behaviors. The numerical results are checked by the mean field theory.