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The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…
We study the effect of metastable states on the relaxation process (and hence information propagation) in locally coupled and boundary-driven structures. We first give a general argument to show that metastable states are inevitable even in…
Community structure is an important factor in the behavior of real-world networks because it strongly affects the stability and thus the phase transition order of the spreading dynamics. We here propose a reversible social contagion model…
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social…
We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or…
A coarse grained description of a two-dimensional prey-predator system is given in terms of a 3-state lattice model containing two control parameters: the spreading rates of preys and predators. The properties of the model are investigated…
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…
We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
We introduce a mathematical model that combines the concepts of complex contagion with payoff-biased imitation, to describe how social behaviors spread through a population. Traditional models of social learning by imitation are based on…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
The non-equilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of metastable configurations that are…
Levels of sociality in nature vary widely. Some species are solitary; others live in family groups; some form complex multi-family societies. Increased levels of social interaction can allow for the spread of useful innovations and…
When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…
Social contagion is a ubiquitous and fundamental process that drives individual and social changes. Although social contagion arises as a result of cognitive processes and biases, the integration of cognitive mechanisms with the theory of…
Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold…