Competition between growth and decline in complex system

Abstract

In daily lives, complex network systems are everywhere. Whether in the social sciences, life sciences or information sciences, there are network structures with different complex topological features and dynamics. By studying the dynamic behaviour of these networks, we could have better understanding of different network structures. However, the impact of competitive relationship dynamics in complex networks on its structure remains to be studied. For instance, in social networks, there are serval impacts of user’s behaviour on the stability of the network: how new users join the network; the connections between new users and old users; and under which circumstance users will leave this network, and how to avoid the ultimate collapse of the network. Therefore, this report focuses on the study of growth-decline competitive relationship in complex networks. In this process, some new nodes will be added to the network, and some new connections will be brought into the network as well. Meanwhile, nodes that do not meet certain conditions will leave the network with a certain probability. By studying the growth and decline process, we can find a dynamic equilibrium point so that the network does not completely collapse. In conclusion, the significance of this project is to help analyse the dynamic behaviour of complex network and how to avoid the ultimate collapse. At the same time, the knowledge I have learnt about complex networks throughout this process is abundant, beneficial and meaningful, and it sharps the skills of understanding, analysing and solving of similar issues.