Related papers: Population dynamics on random networks: simulation…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
We investigate the effects of long-range social interactions in flocking dynamics by studying the dynamics of a scalar model of collective motion embedded in a complex network representing a pattern of social interactions, as observed in…
We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor…
Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Online social networks suffer from explosive user dynamics such as flaming that can seriously affect social activities in the real world because the dynamics have growth rates that can overwhelm our rational decision making faculties.…
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of…
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…
We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably,…
We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…
The population model of Wilson-Cowan is perhaps the most popular in the history of computational neuroscience. It embraces the nonlinear mean field dynamics of excitatory and inhibitory neuronal populations provided via a temporal…
There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…
Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$,…
We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a…