Subspace Of Networks Research Articles

Modular dynamical systems on networks

We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of “fast/slow” variable decompositions or as “abstractions” in the computer science sense of the word.

Synchronizing Subspaces of Networks of Identical Linear Control Systems

Abstract We consider the synchronization problem for networks of linear control systems where the node systems are identical and the interconnection structure is constant. Both synchronizability and stabilizability problem are tackled within the common framework of synchronizing subspaces.

Efficient hexapodal locomotion control based on flow-invariant subspaces

AbstractIn this paper the issue of locomotion control in bio-inspired hexapod structures is considered as a problem of convergence toward flow invariant subspaces in networks of mutually and locally coupled neural units. Since the network topologies used refer to undirected diffusive tree graphs, in this case a unique gain value on the graph connection matrix can be found to guarantee exponential convergence to any desired gait (i.e. phase locked) configuration. Such sufficient condition is exploited for the locomotion control in a hexapod structure. In the paper, after dealing with the sufficient condition above mentioned, both simulation and experimental results on a robotic hexapod structure are reported. Moreover the role of key parameters for insect inspired turning strategies is investigated.

Relaxation- and decoherence-free subspaces in networks of weakly and strongly coupled resonators

We consider a network of interacting resonators and analyze the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces. We investigate two different situations: (i) when the whole network interacts with a common reservoir and (ii) when each resonator, strongly coupled to each other, interacts with its own reservoir. Our main result is that both subspaces are generated when all the resonators couple with the same group of reservoir modes, thus building up a correlation (among these modes), which has the potential to shield particular network states against relaxation and/or decoherence.