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This paper aims to the conditions of traffic flow evolving to stability and the stability of equilibrium under demand time-varying of traffic networks. The general framework of the evolution of flow dynamics by adopting evolutionary game…
One of the holy grails of materials science, unlocking structure-property relationships, has largely been pursued via bottom-up investigations of how the arrangement of atoms and interatomic bonding in a material determine its macroscopic…
Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
A growing body of studies on systemic risk in financial markets has emphasized the key importance of taking into consideration the complex interconnections among financial institutions. Much effort has been put in modeling the contagion…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
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…
We consider network models where information items flow %are sent from a source to a sink node. We start with a model where routing is constrained by energy available on nodes in finite supply (like in Smartdust) and efficiency is related…
In a recent paper, Marr, Muller-Linow and Hutt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula…
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…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions.…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…