Stimulate Parameters Study Of Small World Neural Network

We can describe complex systems of the real world by complex networks, game theoryapplied widely in the biological, economic and other systems. Thereby, the incorporation ofcomplex networks and game theory will give a new idea for researching complex systems.Evolutionary games on graphs presents more abundant physical phenomena compare with thetraditional physical systems.In this paper, we study two models of evolutionary prisoner's dilemma games on the two-layers networks by the Monte Carol numerical simulation method, where the lowerinteraction layer is a square lattice with Von Neumann neighborhood, the upper learning layeris the two-dimensional Newman-Watts small-world networks. The difference between thetwo layers of network can be measured the by the probability p of the Newman-Watts small-world networks, i.e. players have the chance to imitate one except interaction neighborhoods(shortcut neighbors), and the probability is p/(1+p). It is worth noting that our upper learninglayer is very different with one's of M. Ifti etc or Wu etc. In their networks, increasing ofgetting information ability, the each player can learn form their nearest neighbors, nearest andnext-nearest neighbors, and so on. In the Newman-Watts small-world networks, shortcutneighbors can be anyone of the whole nodes except interaction neighborhoods, from this pointof view to consider, the ability of getting information in our network is stronger than one's byM. Ifti etc or Wu etc. But when p=1the numbers of shortcut neighbors are equal to interactionneighborhoods, from this point of view to consider, the quantity of getting information in ournetwork is far less than one's by M. Ifti etc or Wu etc.The modelⅠis the evolutionary prisoner's dilemma games on the two-layers networks.The research shows that it can effectively improve the cooperation when the probability ofimitating shortcut neighbors increasing above10%. The modelⅡ is the evolutionaryprisoner's dilemma games with volunteering on the two-layers networks. The research showsthat the cooperation density have multi-pecks vs. the noise level on the smaller temptationvalue b, but one-pesky on the larger b when shortcut neighbors are absence, but the originalmulti-pecks are instead of one-pesk on the smaller b, on the larger b, it have two-pecks and all strategies density will sharply fluctuating until only one strategy to exist with increasing of pwhen shortcut neighbors are present.