Network seminar 23rd May: Pr. Stefano Boccaletti
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Liubov
May 19, 2024, 2:00:58 AM5/19/24
to network-se...@googlegroups.com, rndapprendre
Dear all,
We are excited to invite you to the seminar by Stefano Boccaletti (Madrid, Spain, Florence, Italy) on 23rd of May at 5pm CET https://en.wikipedia.org/wiki/Stefano_Boccaletti
Register to get a link: https://forms.gle/qbPtMAUY2k1QKeWx5
He will present some works on hypergraphs as well as talk more specifically about the transition to synchronization of networked dynamical systems.
Extended abstract: From brain dynamics and neuronal firing, to power grids or financial markets, synchronization of networked units is the collective behavior characterizing the normal functioning of most natural and man made systems.
As a control parameter (typically the coupling strength in each link of the network) increases, a transition occurs between a fully disordered and gaseous-like phase (where the units evolve in a totally incoherent manner) to an ordered
As a control parameter (typically the coupling strength in each link of the network) increases, a transition occurs between a fully disordered and gaseous-like phase (where the units evolve in a totally incoherent manner) to an ordered
or solid-like phase (in which, instead, all units follow the same trajectory in time).
The transition between such two phases can be discontinuous and irreversible, or smooth, continuous, and reversible.
The first case is known as Explosive Synchronization and refers to an abrupt onset of synchronization following an infinitesimally small change in the control parameter, with hysteresis loops that may be observed as in a thermodynamic first-order phase transition.
The second case is the most commonly observed one, and corresponds instead to a second-order phase transition, resulting in intermediate states emerging in between
the two phases. Namely, the path to synchrony is here characterized by a sequence of events where structured states emerge made of different functional modules
The transition between such two phases can be discontinuous and irreversible, or smooth, continuous, and reversible.
The first case is known as Explosive Synchronization and refers to an abrupt onset of synchronization following an infinitesimally small change in the control parameter, with hysteresis loops that may be observed as in a thermodynamic first-order phase transition.
The second case is the most commonly observed one, and corresponds instead to a second-order phase transition, resulting in intermediate states emerging in between
the two phases. Namely, the path to synchrony is here characterized by a sequence of events where structured states emerge made of different functional modules
(or clusters), each one evolving in unison. This is known as cluster synchronization (CS), and a lot of studies pointed out that the structural properties of the graph are responsible for the way nodes clusterize during CS.
By assuming that, during the transition, the synchronous solution of each cluster does not differ substantially from that of the entire network, I will describe a practical technique which is able to elucidate the transition to synchronization in a generic network of identical systems.
Namely, the method is able to: i) predict the entire sequence of events that are taking place during the transition, ii) identify exactly which graph's node is
By assuming that, during the transition, the synchronous solution of each cluster does not differ substantially from that of the entire network, I will describe a practical technique which is able to elucidate the transition to synchronization in a generic network of identical systems.
Namely, the method is able to: i) predict the entire sequence of events that are taking place during the transition, ii) identify exactly which graph's node is
belonging to each
of the emergent clusters, and iii) provide a well approximated
calculation of the critical coupling strength value at which each
of such clusters is observed to synchronize.
I will also demonstrate that, under the assumed approximation, the sequence of events is in fact universal, in that it is independent on the specific dynamical system
operating in each network's node and depends, instead, only on the graph's structure.
Further, I will clarify that the emerging clusters are those groups of nodes which are indistinguishable at the eyes of any other network's vertex.
I will also demonstrate that, under the assumed approximation, the sequence of events is in fact universal, in that it is independent on the specific dynamical system
operating in each network's node and depends, instead, only on the graph's structure.
Further, I will clarify that the emerging clusters are those groups of nodes which are indistinguishable at the eyes of any other network's vertex.
This
means that all nodes in a cluster have the same connections (and the
same weights) with nodes not belonging to the cluster,
and therefore they receive the same dynamical input from the rest of the network.
As such, synchronizable clusters are subsets more general than those defined by the graph's symmetry orbits, and at the same time more specific than those described by equitable partitions.
As such, synchronizable clusters are subsets more general than those defined by the graph's symmetry orbits, and at the same time more specific than those described by equitable partitions.
On behalf of the seminar organisers,
Liubov
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