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Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…

In order to improve the resilience of computer infrastructure against cyber attacks and finding ways to mitigate their impact we need to understand their structure and dynamics. Here we propose a novel network-based influence spreading…

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…

Convergence of resource allocation algorithms is well covered in the literature as convergence to a steady state is important due to stability and performance. However, research is lacking when it comes to the propagation of change that…

Spreading dynamics has been considered to take place in temporal networks, where temporal interaction patterns between nodes show non-Poissonian bursty nature. The effects of inhomogeneous interevent times (IETs) on the spreading have been…

The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…

The mechanisms of information transmission are investigated in a lattice of coupled continuous maps, by analyzing the propagation of both finite and infinitesimal disturbances. Two distinct regimes are detected: in the former case, both…

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…

Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…

The transient fluctuation of the prosperity of firms in a network economy is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the…

In public railway systems, minor disruptions can trigger cascading events that lead to delays in the entire system. Typically, delays originate and propagate because the equipment is blocking ways, operational units are unavailable, or at…

Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of…

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can…

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…

A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

We consider a sharing economy network where agents embedded in a graph share their resources. This is a fundamental model that abstracts numerous emerging applications of collaborative consumption systems. The agents generate a random…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…