A Study Of Cooperative Evolution Control Problem On Complex Network

The dynamics on network is one of the most popular topics of many scientific disciplines, such as system control, biology, physics, economy and so on. With the combination of complex networks and evolutionary game theory, many scholars focus their attention on the study of the emergence and survival of cooperation behaviors. However, the link between individuals and their positions are not invariable in reality, and the topology of complex network transforms under the influence of evolutionary dynamics. The point of this paper is just that how we can control the topology of complex network evolve to the specified direction through the interaction of individuals and with the help of evolutionary game theory.1. We propose a model to migrate nodes which contain different values on two dimension square lattice. Every node on the lattice has its own attribute which is represented by a number value, and the nodes can only interact with other nodes to find the vertice on the network, which its position coordinate is as much as possible closet to the value that the node have. Thus, by comparing different values of multiple nodes which are located in various positions, and with the range of results, we can change the horizontal coordinate and vertical coordinate of the previous stage node in order to actuate the nodes to migrate on the lattice. An ideal phenomenon that all the nodes which are distinguished by their values distribute on the lattice according a certain rule can be acquired.2. We propose a control strategy which impels nodes of network to connect with a specific node that we have specified with the perspective of spatial evolutionary public goods game. It is often the case that rational individuals will adjust their connectivity in commercial or social activities for maximizing their payoffs. In this process, we can observe that individuals always gather around a leader or a competitive individual who can bring them more benefits. Inspired by this, a node is specified and given a larger enhancement factor which reflects his advantages over others. Then we employ a payofforiented preferential rewire strategy so that individuals can have a chance to connect with others who can bring them more benefits. The results illustrate that this strategy not only ensure the promotion of cooperation but also increase the degree of the specified node.Meanwhile, by analyzing the results and parameters, we can prove that a cooperative environment and a relatively lower rewire frequency can help this strategy work effectively.3. We build a spatial evolutionary game theory simulation platform which is running on an online server. Users only need to open their browser and type the address to connect the online simulation platform and then they can run their spatial public goods game simulation on this platform. When the simulation is terminated, they can check the answer on the Internet. This platform can help beginners have an initial and visual understanding of the spatial evolutionary public goods game.