# Collective Dynamics from Stochastic Process Algebras

Precise interaction of individuals coupled with analysis of the dynamic behaviour at the level of populations.

Process calculi have traditionally been discrete-state modelling tools. These give precise characterisations of systems with a small number of abstractly-described components. However, such models cannot scale to large numbers of closely-described components. An alternative semantics which is based on continuous-state representations can scale to describe large populations of components but this comes at the cost of using an approximation of the true (discrete) behaviour. Such continuous-state semantics have been provided for the process algebra PEPA, and its recent biological dialect Bio-PEPA. These have given rise to applications in software systems, scalability analyses, systems biology, epidemiology and crowd dynamics.

There is potential for several PhD projects arising from this theme. For example, the feasibility of developing good models of collective behaviour for systems with distinct spatial compartments or regions is yet to be fully explored. There is also several interesting questions with respect to heterogenous systems in which only some subpopulations scale uniformly but which nevertheless exhibit collective behaviour overall. Another example, would be the development of suitable query languages and logics to interrogate the behaviour of such systems.

### Prospective Supervisors