Related papers: Stability of a Stochastic Ring Network
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become…
Gradual advancement of control technology gives rise to the studies of the stability of linear systems. The stability of the linear multiagent system is motivated by increasing utilization of agent dynamics together with the number of…
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and…
The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state…
Reasonably large perturbations may push a power grid from its stable synchronous state into an undesirable state. Identifying vulnerabilities in power grids by studying power grid stability against such perturbations can aid in preventing…
A new framework to perform routing at the Autonomous System level is proposed in this paper. This mechanism, called Chain Routing, uses complete orders as its main topological unit. Since complete orders are acyclic digraphs that possess a…
We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…
According to the May-Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to…
Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to…
We consider a network of event-based systems that use a shared wireless medium to communicate with their respective controllers. These systems use a contention resolution mechanism to arbitrate access to the shared network. We identify…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…