## Complex Systems

I understand and support the search for the deepest secrets of nature, in terms of fundamental laws that could explain everything. But I feel that this reductionist mindset does not give due consideration to complex phenomena. As P. W. Anderson puts it: More is different. Macroscopic objects and processes are not merely aggregates of fundamental particles, and systems don’t always exist in equilibrium. There are emergent phenomena at different scales and we need to embrace complexity in order to ‘explain’ them.

I think of complex systems analysis in two ways. In one, we model a system using some knowledge of its inner workings and try to mimic the observed qualitative behaviour. In another, we start from data generated by the system and detect signatures of underlying dynamics in order to get clues of the inner workings. I have followed both in the past few years, with the common framework of networks. I have been exploring what happens when nonlinear systems are coupled in a specific configuration, and I have explored complex network approaches in data, such as recurrence networks. I find networks intuitive in principle, but their extensions and applications intriguing.

## Complex systems as networks

Complex systems are characterized by interacting components that give rise to emergent behaviour that cannot be explained by their individual dynamics. This feature makes the study of complex systems difficult since you cannot “reduce” their dynamics to their components in isolation. Perhaps the simplest representation of these systems is in terms of complex networks, where the components are nodes, and interactions, edges.

## Recurrence Networks

Recurrence Networks develop on the foundations of dynamical systems theory. Essentially, any given dynamical system will inhabit some parts of the associated phase space/state space, depending on the parameters governing the system and initial conditions, in time. Recurrence Networks (RNs) are constructed from proximity analysis of points in the phase space.