Related papers: A Continuous Threshold Model of Cascade Dynamics
Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…
Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus.…
Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus…
We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary…
This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…
Social networks of engagement sometimes dramatically collapse. A widely adopted paradigm to understand this catastrophe dynamics is the threshold model but previous work only considered the irreversible K-core pruning process and the…
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
We propose an online detection procedure for cascading failures in the network from sequential data, which can be modeled as multiple correlated change-points happening during a short period. We consider a temporal diffusion network model…
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
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…
Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We…
A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple {\it initiators} trigger the cascade, and where all…
We develop a framework for studying and quantifying the risk of cascading failures in time-delay consensus networks, motivated by a team of agents attempting temporal rendezvous under stochastic disturbances and communication delays. To…
Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this…
This paper studies the operation of multi-agent networks engaged in multi-task decision problems under the paradigm of simultaneous learning and adaptation. Two scenarios are considered: one in which a decision must be taken among multiple…
This paper proposes a new lens for studying threshold games played on networks when the thresholds are heterogeneous. These are games where agents have two possible actions, and prefer action 1 if and only if enough of their neighbours…