Symmetry-Breaking Game And Cascading Failures In Complex Networks

Complex networks are commonly used to denote real systems. In a complex network, nodes represent units in the system and edges represent connections between different units. In many real systems, the nodes are individuals with ability of behavioural decision. When there exists an interaction between two nodes, each node will take egoistic action to make the interaction more favourable to itself, which break the symmetry of the interaction. For instance, there are a lot of data packets transmitted among different routers in a mesh wireless network. When there exists information congestion on a router, this node always hopes the load assumed on itself can be redistributed to other nodes while reducing the data packets transmitted from other routers to keep the efficiency of this node not decline or breakdown. Once some nodes become overloaded or faulted, the load on them will be redistributed to others, which easily leads the network to cascade or avalanche. However, existing research on cascading failures has focused on exploring flow variation and congestion control from the view of topological structure rather than the effect of the interaction among nodes. Based on this, our group construct corresponding model to characterize the dynamical behavior of symmetry-breaking of the interaction between nodes and investigate its impact on the network robustness through cascading failures.In this thesis, we first reveal the phenomenon of symmetry-breaking of the interaction between nodes. According to the features of autonomy, rationalism and egoistic behaviors in the interaction, the theory of symmetry-breaking game has been built to characterize the dynamical process of symmetry-breaking of interaction between nodes. The rationality of the model and the main factors affecting the degree of the symmetry has been discussed in theory. To investigate the effect of the asymmetry factors on the outcome of the game, the simulation of the game has been carried on ER network, NW network and BA network, respectively. The simulation results verify the correctness of this theory and the relationship between the asymmetry factors and the symmetry-breaking of the interaction.Afterwards, our group explore the relations between the symmetry-breaking of interaction and cascading propagation during the load redistribution, which explores the intrinsic link between game dynamics and cascading dynamics. We construct a cascading model on symmetry-breaking game and simulate the cascading propagation on BA network and Autonomous Systems. By adjusting the asymmetry factors of initial load and strategies’ payoff, the variation of the largest connected scale and the cascading persistent duration has been observed under different kinds of attack. Finally, based on the time features of the cascading evolution, a mitigation mechanism is presented to reduce the cascading losses by means of adjusting the asymmetry parameters in real time. This outcome gives important theory for emergent response and control of cascading failures under the major disaster.