## MathsNet: Research Student Directory

Name | Rose, Alexander |
---|---|

Group | Industrial and Applied Mathematics |

Room | B8, Math Sci |

Telephone | +44 (0) 115 95 14912 [direct dial] |

Thesis Title | Form and function of dynamical networks |

Thesis Abstract | Networks - systems of interconnected elements - form structures through which information or matter is conveyed from one part of an entity to another, and between autonomous units. The form, function and evolution of such systems are affected by interactions between their constituent parts, and perturbations from an external environment. The challenge in all application areas is to model effectively these interactions which occur on different spatial- and time-scales, and to discover how i) the micro-dynamics of the components becomes expressed macroscopically as a function of the network architecture ii) the network is affected by the external environment(s) in which it is embedded. Thus the optimal performance of a network is dependent its internal structure, the dynamical processes on it, and its connection to the outside world. If the dynamical processes are agent based, then these can adapt according to specified rules and the project will investigate strategies for how the dynamical network can be made to perform macroscopically in an optimal way. The ‘price of anarchy’ measures the increase in global cost that results from agents on the network choosing their own behaviours rather than adhering to that which obtains the optimum. In the first instance, the time taken for information to propagate across a network will be investigated, and the price of anarchy derived from this will be compared for directed graphs having regular lattice, Poisson and small-world structures. The calculations will repeated for undirected graphs, which enables information to circulate within for longer. Thus the influence of the network structure will be characterized. The calculations can then be repeated for the situation when the dynamics of the agents becomes adaptive, either deterministically (i.e. through dictat) or cooperatively through nearest neighbour influence. Thus the relative importance of architecture and local behaviour on overall function can be gauged. |

School contact information | School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD UK Tel: +44 (0) 115 951 4949 Fax: +44 (0) 115 951 4951 |