Francesco Sorrentino

Assistant Professor

University of New Mexico

Research

I work in the area of dynamical systems and controls. Most of my research has to do with networks of coupled dynamical systems. These are some of the problems I am working or have worked on:

• Networks of synchronizing dynamical systems: analysis of the topological properties of complex networks and study of role of the topology in affecting the synchronization dynamics taking place on them. Analysis of the network synchronizability in presence of degree correlation by means of the Master Stability Function theory.
• Pinning control of dynamical networks: role of control on network synchronization; definition of strategies of distributed control on networks (pinning control); effects of the network structural properties (degree distribution, degree correlation, community structure) in affecting the network controllability.
• Study of synchronization in networks of groups formed of different systems: definition of a new Master Stability Function to analyze the network synchronizability in case of networks formed of groups of (totally) different systems.
• Adaptive synchronization: definition of adaptive strategies to synchronize a time varying complex network in the presence of delays and when global information on the local structure of the network is not available. Experiments are being carried out at the Institute for Research in Electronics and Applied Physics at the University of Maryland to test the effectiveness of our adaptive synchronization technique to synchronize networks of coupled opto-electronics systems.
• Sensor Network identification (learning the topology of a sensor network): definition of adaptive strategies aimed at identifying the time evolution of the couplings associated with the links of a complex sensor network from dynamical information.
• Identification and forecast of unknown dynamical systems: definition of an adaptive strategy aimed at reconstructing all the parameters of the equations of a given unknown chaotic system from dynamical information. Use of this technique to forecast the future behaviour of the unknown system.
• Study of congestion in communication networks: definition of appropriate indices to measure the congestion of a complex network; effects of the statistical properties of the traffic and of the topological proprieties of complex networks on their communication performance; analysis of packet transport dynamics in communication networks.
• The dynamics of large networks of coupled neurons: We are interested in the emergence of synchronization in large ensembles (the brain has about 1012 neurons) of coupled neurons. Particular emphasis is on the role of synaptic plasticity and its relevance in generating coherent behavior of the brain. Another subject of current investigation is the role of excitatory as well as inhibitory connections in affecting the dynamic range of a neural network.
• Evolutionary Game Theory on Networks: We study a network of coupled agents playing the Prisoner's Dilemma game, in which players are allowed to pick a strategy in the interval [0,1], with 0 corresponding to defection, 1 to cooperation, and intermediate values representing mixed strategies in which each player may act as a cooperator or a defector over a large number of interactions with a certain probability. We consider that each player chooses his/her strategy in a context of limited information. We formulate a deterministic model for the evolution of strategies driven by the payoffs of the players. We show both analytically and numerically that the final strategies depend both on the network structure and on the choice of the parameters of the game.
• Synchronization of hypernetworks: We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each of which corresponds to a distinct type of interaction), and we refer to such a system as a hypernetwork. Applications include neural networks formed of both electrical gap junctions and chemical synapses, the coordinated motion of shoals of fishes communicating through both vision and flow sensing, and hypernetworks of coupled chaotic oscillators.
• Identification of unknown communication delays: We consider two bidirectionally coupled systems (mobile platforms) that seek to synchronize through a signal that each system sends to the other one and is transmitted with an unknown time-varying delay. We show that a decentralized agreement protocol based on an appropriate adaptive strategy can be devised that is successful in dynamically identifying the time-varying delay and in synchronizing the two systems. As a reference application, we consider the problem of identifying the communication-delay between two autonomous moving platforms. We assume that two identical chaotic oscillators are installed at each platform and that these chaotic systems seek to synchronize via a signal broadcast from one platform to the other (and viceversa).