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Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
We study the dynamics of the Internet topology based on the empirical data on the level of the autonomous systems. It is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
Dynamic network analysis has found an increasing interest in the literature because of the importance of different kinds of dynamic social networks, biological networks, and economic networks. Most available probability and statistical…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class.…
We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states.…
An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out,…
Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to…
We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure-centrality. We show that the degree of…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
Growing evidence suggests that the macroscopic functional states of urban road networks exhibit multistability and hysteresis, but microscopic mechanisms underlying these phenomena remain elusive. Here, we demonstrate that in real-world…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…
We explore packet traffic dynamics in a data network model near phase transition point from free flow to congestion. The model of data network is an abstraction of the Network Layer of the OSI (Open Systems Interconnection) Reference Model…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…