This thesis explores aspects of model specification and analysis for population dynamics which arise when modelling complex interactions and communication structures in
agent or component collectives. The motivating examples come from the design of
man-made systems where the optimal parametrisations for the behaviours of agents or
components are not known a priori. In particular, we introduce a formal modelling
framework to support the specification of control problems for collective dynamics in
a high-level process algebraic language. A natural choice for the underlying semantics
is to consider continuous time Markov decision processes due to their close relation to
continuous time Markov chains that have traditionally been used as the mathematical
model in numerous high-level modelling languages for stochastic dynamics.
Although the theory of the resulting decision processes has a long history, the
practical considerations, like computation time, present challenges due to the problem
of state space explosion when considering large systems with complex behaviours. State
space explosion problems are especially apparent in formal modelling paradigms where
the specification of models usually happens at a component or an agent level in terms
of a discrete set of states with defined rules for composing the specified behaviours into
the dynamics of a system. Such specifications often give rise to very large models which
are costly to analyse in full detail. However, when analysing models of collectives we
are usually interested in the resulting macro-scale dynamics in terms of some aggregate
measures. With that in mind, the second aspect of analysing collective dynamics that
is considered in this thesis relates to fluid, linear noise and moment closure-based
approximation methods which aim to give a good representation of the macro-scale
dynamics of the models while being computationally less costly to analyse.
We address a class of models where the population structure results from the assumption that components or agents can only be distinguished from each other based on
the state they are in and focus on the particular cases where the population dynamics
can be separated into a discrete set of modes. Our study of these models is motivated
by considering information propagation via broadcast communication where the behaviour of components can change drastically when new information is received from
the rest of the population. We consider existing approximation methods for resulting
stochastic processes and propose a novel approach for applying these methods to models incorporating broadcast communication where each level of information available to
the collective corresponds to a discrete dynamic mode. The resulting approximations
combine continuous dynamics with discrete stochastic jumps and are not immediately
simple to treat numerically. To that end we propose further approximations that allow for a computationally efficient analysis. Finally, we demonstrate how the formal modelling framework in conjunction with the developed approximation methods can
be used for an example in policy synthesis
