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This brief paper further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive…
We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…
Learning the dynamics of complex systems features a large number of applications in data science. Graph-based modeling and inference underpins the most prominent family of approaches to learn complex dynamics due to their ability to capture…
Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…
Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent…
For a network of interconnected nonlinear dynamical systems an adaptive leader-follower output feedback synchronization problem is considered. The proposed structure of decentralized controller and adaptation algorithm is based on…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to…
Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…
Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
I analyse a model of an evolving network represented as a directed graph; each node corresponds to one molecular species and the links to catalytic interactions between species. Over short timescales the graph remains fixed while relative…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve…
The observed long-range spatiotemporal correlations of real world dynamical systems is governed by quantumlike mechanics with inherent non-local connections. In summary, microscopic scale local fluctuations form a unified self-organized…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…