Complex Dynamics on Networks

Networks and graphs are the most general mathematical description of a set of elements connected pairwise by a relation. Therefore, it is not surprising that graph theory has been successfully applied to a wide range of very different disciplines, from physics to biology, to social science, computing, psychology, economy and chemistry.

In recent times, physicists have been mainly interested in networks as models of complex systems and they have used them to describe condensed matter structures such as disordered materials, glasses, polymers, biomolecules. More recently, networks have become the main language for the description of communication networks, webs, social and economic systems, power grids, statistical models of algorithms, and many others interdisciplinary frameworks.

The function of networks in physics, however, is not purely descriptive. Geometry and topology have a deep influence on the physical properties of complex systems. The network structure can indeed affect the dynamical and thermodynamical behaviour of the system it describes, and can give rise to surprising collective effects.

Synchronization on Neural Networks

In Parma, we are studying dynamical models for synchronization on neural networks in collaboration with the University of Granada. We are investigating spatially extended stochastic bistable systems, with the specific purpose of understanding some of the fundamental functional features of neural networks. Our aim is to give the description of some general mechanisms, in the simplest model and subsequently progressively make this model closer and closer to the physiology of neural cortical tissues, according to the experimental results.

Some of the topics we address are the role of inhibition and of synaptic plasticity as well as the function played by the structural properties of the network. Moreover we are focusing on the aspects of criticality that have been shown to describe some characteristics of the neural activity, aiming at specifying some important details and properties found in this framework and gaining deeper insight in the mechanisms by which the system self-organizes to a singular point.

Epidemics on Complex Networks

In Parma, we are dealing with the modelling of epidemic spreading on complex temporal networks. We are investigating the dynamics of human interaction networks and its effects on epidemic spreading. Some of the topics we address are the role of memory, non-Markovianity and burstiness in network evolution and in epidemic spreading.

Moreover, we are focusing on adaptive temporal networks which model the adaptive behaviours of populations exposed to epidemics, taking into account behavioural changes due to awareness, symptoms onset and the attempt to reduce the risk of infection. We model and compare several epidemic control and containment measures such as quarantine, contact tracing and sick-leave, analyzing their effectiveness in reducing the impact of an epidemic. We are also applying our adaptive temporal network models to the COVID-19 pandemic, modelling some crucial features of COVID-19 transmission and effective control interventions.

On this topic we are collaborating with national and international groups such as the EPIcx lab at INSERM - Institut national de la santé et de la recherche médicale, Sorbonne Université in Paris, the MoBS Labs at Boston Northeastern University and the Institute for Scientific Interchange in Torino.

Random walks, anomalous diffusion and large deviations effects

How does matter diffuse in a complex material?

How is information transmitted in a complex network, can a disease spread over an entire population?

These are typical non equilibrium questions that we ask in our research. The effect of large fluctuations on these processes is extremely important. In particular, complex systems can often experience Big Jumps, that is sudden huge events that can completely shift the non equilibrium process. Identifying these events and develop a mathematical framework to deal with them is what we do.

Fundamental Aspects of Nonequilibrium Quantum Mechanics

Complex systems and their modeling are interesting simply because matter is typically complex. On small scales, quantum mechanics describes interactions and dynamics.

One typical example of a complex quantum system are photosynthetic molecules (complexes) in which transport properties seem to be governed by quantum mechanical interference. Strong correlations between the constituents make even "small" systems very complicated. In the helium atom, for instance, classical three-body chaos turns into complicated ionization spectra. The modern experimental tools of atom optics allow for a bottom-up construction of strongly correlated many-body quantum systems.

We are studying their behavior on the level of single atoms and their interaction. Ongoing collaborations with experimental groups the world over enrich our research on fundamental aspects of quantum transport and its control in view of applications in atomtronics and quantum information. You can found further information at Complex Dynamics in Quantum Systems


  • M. Mancastroppa, A. Guizzo, C. Castellano, A. Vezzani, R. Burioni
    "Sideward contact tracing and the control of epidemics in large gatherings", ArXiv:2110.04742 (2021)

  • V. Buendía, P. Villegas, R. Burioni, M.A. Muñoz
    "The broad edge of synchronisation: Griffiths effects and collective phenomena in brain networks", ArXiv:2109.11783 (2021)

  • Selected recent publications

  • V. Buendía, P. Villegas, R. Burioni, and M. A. Muñoz
    "Hybrid-type synchronization transitions: Where incipient oscillations, scale-free avalanches, and bistability live together", Phys. Rev. Research 3, 023224 (2021)

  • M. Stucchi, F. Pittorino, M. di Volo, A. Vezzani, R. Burioni
    "Order symmetry breaking and broad distribution of events in spiking neural networks with continuous membrane potential", Chaos, Solitons Fractals 147, 110946 (2021)

  • M. Mancastroppa, C. Castellano, A. Vezzani, R. Burioni
    "Stochastic sampling effects favor manual over digital contact tracing", Nature Communications 12, 1919 (2021)

  • E. Ubaldi, R. Burioni, V. Loreto, F. Tria
    "Emergence and evolution of social networks through exploration of the Adjacent Possible space", Communications Physics 4, 28 (2021)

  • M. Mancastroppa, R. Burioni, V. Colizza, A. Vezzani
    "Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks", Phys. Rev. E 102:020301(R) (2020) - Editors' Suggestion

  • F. Pinotti, L. Di Domenico, E. Ortega, M. Mancastroppa, G. Pullano, E. Valdano, P. Boelle, C. Poletto, V. Colizza
    "Tracing and analysis of 288 early SARS-CoV-2 infections outside China: A modeling study", PLOS Medicine 17(7):e1003193 (2020)

  • V. Buendia, S. di Santo, P. Villegas, R. Burioni, M. A. Muñoz
    "Self-organized bistability and its possible relevance for brain dynamics", Phys. Rev. Research 2, 013318 (2020)

  • R. Burioni, A. Vezzani
    "Rare events in stochastic processes with sub-exponential distributions and the big jump principle", J. Stat. Mech., 034005 (2020)

  • A. Vezzani, E. Barkai, R. Burioni
    "Rare events in generalized Lévy Walks and the Big Jump principle", Sci. Rep. 10, 2732 (2020)

  • W. Wang, A. Vezzani, R. Burioni, E. Barkai
    "Transport in disordered systems: The single big jump approach", Phys. Rev. Research 1, 033172 (2020)

  • F. Cescatti, M. Ibáñez-Berganza, A. Vezzani, R. Burioni
    "Analysis of the low-temperature phase in the two-dimensional long-range diluted XY model", Phys. Rev. B 100 (5), 054203 (2019)

  • V. Buendía, P. Villegas, S. di Santo, A. Vezzani, R. Burioni, M.A. Muñoz
    "Jensen's force and the statistical mechanics of cortical asynchronous states", Sci. Rep. 9, 15183 (2019)

  • A. Vezzani, E. Barkai, R. Burioni,
    "Single-big-jump principle in physical modeling", Phys. Rev. E 100 (1), 012108 (2019)

  • M. Mancastroppa, A. Vezzani, M. A Muñoz, R. Burioni,
    "Burstiness in activity-driven networks and the epidemic threshold", J. Stat. Mech. 053502 (2019)

  • F. Petiziol, B. Dive, F. Mintert, S. Wimberger,
    "Fast adiabatic evolution by oscillating initial Hamiltonians" Phys. Rev. A 98, 043436 (2018)

  • M. Tizzani, S.Lenti, E.Ubaldi, A. Vezzani, C. Castellano, R. Burioni,
    "Epidemic spreading in temporal networks with memory", Phys. Rev. E 98, 062315 (2018)

  • S. di Santo, P. Villegas, R. Burioni, M.A. Munoz,
    "Landau Ginzburg Theory of Cortex Dynamics: Scale free avalanches emerges at the edge of synchronization", PNAS 1712 989115 (2018)

  • F. Pittorino, M. Di Volo, M. Ibanez Berganza, A Vezzani, R. Burioni,
    "Chaos and Correlated avalanches in Neural Networks with synaptic plasticity", Phys. Rev. Lett. 118, 098102 (2017)

  • D. Witthaut, S. Wimberger, R. Burioni, M.Timme,
    "Classical Synchronization indicates persistent entanglement in isolated quantum systems", Nature Communications ncomms14829 (2017)

  • M. Weiss, C. Groiseau, W.K Lam, R. Burioni, A. Vezzani, G.S. Summy, S. Wimberger,
    "Steering random walks with kicked ultracold atoms", Phys. Rev. A 92 033606 (2015)

  • R. Burioni, E. Ubaldi, A. Vezzani,
    "Superdiffusion and Transport in 2d-systems with Levy Like Quenched Disorder", Phys. Rev. E 89 022135-022145 (2014)

  • P. Bernabo', R. Burioni, S. Lepri, A. Vezzani,
    "Anomalous transmission and drifts through one-dimensional Levy structures", Chaos, Solitons & Fractals 67, 1119 (2014)