CompSci2NetSci: building the next generation of evolving complex networks

A complex network can be interpreted from the graph theory perspective as a large number of interacting and interdependent systems (nodes) coupled in a non-trivial and non-regular way (links). Typically, the nodes’ dynamics are not considered, or just simplified. The tendency has been to use mathematical measurements to describe the topological properties of the network (especially, related to size, density and connectivity). This approach is more statistical than behavioural, and consequently has important limitations in the analysis of collective emergent dynamical properties, and network evolution and adaptation.

The main goal of this research is to propose a new generation of complex network models to analyse the pattern in different evolving and adaptive dynamical processes, in which the topology is directly dependent on the dynamics of the nodes. Pre-existing models of complex networks are not appropriate for this purpose. Furthermore, they fail to effectively reproduce a key aspect of complex networks: switching/discontinuous dynamical processes and modularly varying goals. This project will solve this by combining hybrid automaton models and control engineering paradigms. A hybrid automaton is a computational-oriented model for hybrid systems. Essentially this is a finite state machine that considers a dynamical subsystem in each discrete state.

The framework proposed here is general and applicable to a broad class of physical, biological and engineering systems. Depending on the student’s interests, different application domains can be explored. This research would be part of the project DYVERSE (DYnamical-driven VERification of Systems with Energy considerations).