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We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system…
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
The time-dependent vulnerability of synchronized states is shown for a complex network composed of electronic circuits. We demonstrate that disturbances to the local dynamics of network units can produce different outcomes to…
We study the effect of coupling delay in a regular network with a ring topology and in a more complex network with an all-to-all (global) topology in the presence of impurities (disorder). We find that the coupling delay is capable of…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to $s$. We find theoretically and via simulation that in complex networks with random…
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be…
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory. The stable steady states of these dynamics…
Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that…
We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the…
Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the nucleus isthmi. Extracellular stimulation combined with intracellular recordings reveal a range of signal…
The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
Leveraging a validated set of reconstructed Lightning Network topology snapshots spanning five years (2019-2023), we computed 47 computationally intensive metrics and network attributes, enabling a comprehensive analysis of the network's…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…