Related papers: True Nonlinear Dynamics from Incomplete Networks
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Various natural and engineered systems, from urban traffic flow to the human brain, can be described by large-scale networked dynamical systems. These systems are similar in being comprised of a large number of microscopic subsystems, each…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
In this article, we consider a dynamic model of a three-phase power system including nonlinear generator dynamics, transmission line dynamics, and static nonlinear loads. We define a synchronous steady-state behavior which corresponds to…
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…