Learning in adaptive networks: analytical and computational approaches
The dynamics on networks and the dynamics of networks are usually entangled with each other in many highly connected systems, where the former means the evolution of state and the latter means the adaptation of structure. In this thesis, we will study the coupled dynamics through analytical and computational approaches, where the adaptive networks are driven by learning of various complexities. Firstly, we investigate information diffusion on networks through an adaptive voter model, where two opinions are competing for the dominance. Two types of dynamics facilitate the agreement between neighbours: one is pairwise imitation and the other is link rewiring. As the rewiring strength increases, the network of voters will transform from consensus to fragmentation. By exploring various strategies for structure adaptation and state evolution, our results suggest that network configuration is highly influenced by range-based rewiring and biased imitation. In particular, some approximation techniques are proposed to capture the dynamics analytically through moment-closure differential equations. Secondly, we study an evolutionary model under the framework of natural selection. In a structured community made up of cooperators and cheaters (or defectors), a new-born player will adopt a strategy and reorganise its neighbourhood based on social inheritance. Starting from a cooperative population, an invading cheater may spread in the population occasionally leading to the collapse of cooperation. Such a collapse unfolds rapidly with the change of external conditions, bearing the traits of a critical transition. In order to detect the risk of invasions, some indicators based on population composition and network structure are proposed to signal the fragility of communities. Through the analyses of consistency and accuracy, our results suggest possible avenues for detecting the loss of cooperation in evolving networks. Lastly, we incorporate distributed learning into adaptive agents coordination, which emerges as a consequence of rational individual behaviours. A generic framework of work-learn-adapt (WLA) is proposed to foster the success of agents organisation. To gain higher organisation performance, the division of labour is achieved by a series of events of state evolution and structure adaptation. Importantly, agents are able to adjust their states and structures through quantitative information obtained from distributed learning. The adaptive networks driven by explicit learning pave the way for a better understanding of intelligent organisations in real world.