Evolutionary Dynamics - A complex systems approach to the study of evolution of dynamical networks

Recently, the development of networks theory has allowed for scientific and conceptual breakthroughs in different areas of the human knowledge, and a new vision of the world has emerged. Indeed, it is now extremely common to adopt a description of human and economic relationships in terms of a set of complex interactions between the elements that belong to the whole system.

In the past years, many studies have focused on network dynamics. In this context, a new model known as Tangled Nature model has been proposed to describe the evolution of ecosystems and to understand how the individual based interactions influence the macroscopic complex behaviour of the network. Since then, many variations on the model have been proposed, and it has also been successfully applied to describe the interactions between financial markets. We believe that it may be interesting to look at such models and analyse the behaviour and the dynamics of networks by a new perspective, that involves the introduction of concepts that belong to information theory. In particular, it would be interesting to identify a mathematical object that describes quantitatively the ability of the system to adapt to external perturbations, and to evolve. This would be of crucial importance for the understanding of the mechanisms that are behind the evolution of life on earth. Furthermore, it would give more insight about how some kind of networks - for instance economic networks - evolve in time, and how they acquire more stability and adaptability to external perturbations.

The potential applications of the research cover a wide range, spanning from theoretical ecology to financial networks. In particular, this study may be useful to determine the stability of such systems through the study of their inherent dynamics, and potentially to prevent catastrophic events such as a mass extinction of species or an economic crisis.