FocusResearch on Dynamics of Complex Systems at Politecnico di Milano concerns several aspects of the theoretical and numerical analysis of nonlinear dynamical systems, both as individual units and as networks of interconnected units. In the case of isolated systems, the focus is on the use of nonlinear systems theory, in particular bifurcation analysis, to classify the behaviours of the system and to understand the critical transitions occurring when parameters are varied. In the case of networks of systems, the focus is on the mutual interactions between the topological structure and the emerging collective dynamics. Applications in very diverse fields are considered, including e.g. biology, epidemiology, social sciences, and vehicle dynamics.
Most relevant research achievements
Bifurcations in smooth and non-smooth systems: theory and numerical tools
The analysis of the transitions occurring in a systemís behaviour when parameters are varied is a fundamental step in the understanding of its dynamics. It allows one to list the catalogue of qualitatively similar behaviours, providing a powerful tool for analysis, design, and control. Bifurcation theory is the main tool of investigation. The groupís research achievements include significant theoretical advances and software implementations of numerical algorithms.
Modelling and analysis of innovation and competition processes
Innovation and competition processes are ubiquitous in many fields of science. They are responsible for evolutionary dynamics entrained by innovative changes in the characteristics of individual agents and by competitive interactions promoting the best performances. Genetic mutations and natural selection play such roles in biology, but the scope of the evolutionary paradigm well embraces social sciences, economics, engineering, and computer science. Methodological and applied contributions have been given to Adaptive Dynamics, one of the most flexible modelling approaches to innovation and competition processes, and the first comprehensive book on the subject has been written.
Interaction of topology and dynamics in complex networks
The collective dynamics of systems over networks may be strongly influenced by the topology of the interconnections. An effective method has been devised for finding and testing community structures (i.e., dense clusters of nodes), with effective applications in economics and finance. Subtle and unexpected interactions between topology and dynamics also characterize contact processes, i.e., epidemic spreading over networks.
Synchronization in networks of oscillators
Significant findings have been obtained on synchronization in networks of resource-consumer systems: if consumers are exploited by a top-predator, their dispersal is the most effective mechanism for promoting synchronization. If all systems are forced by the same chaotic input (environment), synchronization is possible if the complex behaviours of resources and consumers are only due to the environment itself. If demographic parameters and dispersal are subject to mutation-selection processes, then evolution drives these networks toward weak forms of synchrony.