Related papers: Linear stability analysis for large dynamical syst…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…
Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement,…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…