Related papers: Single-Target Networks
We investigate the possibility that for any given reaction rate vector $k$ associated with a network $G$, there exists another network $G'$ with a corresponding reaction rate vector that reproduces the mass-action dynamics generated by…
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory…
We consider the dynamics of a reaction-diffusion system on a multigraph. The species share the same set of nodes but can access different links to explore the embedding spatial support. By acting on the topology of the networks we can…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
Terrorism instills fear in the minds of people and takes away the freedom of individuals to act as they will. Terrorism has turned out to be an international menace today. Here, we study the terrorist attack incidents which occurred in the…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…
The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to…
We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices $i\in I$ are interpreted as agents, and the edges $c\in C$ as contracts that can be concluded between agents. The preferences of each agent…
We search for conditions under which a characteristic time scale for ordering dynamics towards either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…
We study dynamical transportation networks in a framework that includes extensions of the classical Cell Transmission Model to arbitrary network topologies. The dynamics are modeled as systems of ordinary differential equations describing…
Let $G$ be a graph, which represents a social network, and suppose each node $v$ has a threshold value $\tau(v)$. Consider an initial configuration, where each node is either positive or negative. In each discrete time step, a node $v$…
We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node…
We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…