Related papers: A nonlinear graph-based theory for dynamical netwo…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…
The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects…
In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
An observability condition number is defined for physical systems modeled by network dynamics. Assuming the dynamical equations of the network are known and a noisy trajectory is observed at a subset of the nodes, we calculate the expected…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that when a quantum network is described by such a graph, the network is efficiently controllable, in…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
A method of network reconstruction from the dynamical time series is introduced, relying on the concept of derivative-variable correlation. Using a tunable observable as a parameter, the reconstruction of any network with known interaction…
We analyze the problem of network identifiability with nonlinear functions associated with the edges. We consider a static model for the output of each node and by assuming a perfect identification of the function associated with the…