Related papers: Linear dynamical systems on graphs
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
Multiplex networks (a system of multiple networks that have different types of links but share a common set of nodes) arise naturally in a wide spectrum of fields. Theoretical studies show that in such multiplex networks, correlated edge…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
An explicit expression for the cofactor related to an irreducible invariant algebraic curve of a polynomial dynamical system in the plane is derived. A sufficient condition for a polynomial dynamical system in the plane to have a finite…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without…
Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by preintegration and exact…
A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over…
A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li\'{e}nard dynamical systems $x_t=y$,…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…