Related papers: The phase diagram of random threshold networks
A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter…
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…
DC networks play an important role within the ongoing energy transition. In this context, simulations of designed and existing networks and their corresponding assets are a core tool to get insights and form a support to decision-making.…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs.…
Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated…
We investigate cascade dynamics in threshold-controlled (multiplex) propagation on random geometric networks. We find that such local dynamics can serve as an efficient, robust, and reliable prototypical activation protocol in sensor…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also…
We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…
Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that…
We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…