The fate of real systems
Improving our understanding of real-world networks with sophisticated analyses of realistic complications.
To understand a theoretical complex network, with simplified connections and structure, is no mean feat. It is another challenge entirely to shift that network into the real world, with all of its complications, and repeat the trick. However, it is vital to find a way to use what we have learnt from the solutions of idealised networks and extend them to practical scenarios.
In this project, we investigate how networks grow, synchronise and become unstable or disordered under real-world conditions. We tackle complications such as finite carrying capacity, and small-scale perturbations which lead to transient dynamics. These technicalities require fine-grained insight into the time evolution of the networks and sophisticated methods such as transfer operator analysis to get a handle on all of the moving parts.
The ability to solve realistic complex networks will make it possible to predict the behaviour of real-world systems under the imperfect stresses and changes that they are subjected to. These results will be of importance to studies of populations, ecosystems and financial systems, in order to inform societal and political decisions.
An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.
An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.
The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.
A transfer operator formalism solves the macroscopic dynamics of disordered Ising chain systems which are relevant for ageing phenomena.