Game theory is one of the key paradigms behind many scientific disciplines from biology to
behavioral sciences to economics. In its evolutionary form and especially when the …

Spatially extended population dynamics models that incorporate demographic noise serve
as case studies for the crucial role of fluctuations and correlations in biological systems …

We provide an overview of recent research on belief and opinion dynamics in social
networks. We discuss both Bayesian and non-Bayesian models of social learning and focus …

One of the major challenges in modern biology is to understand how the molecular
components of a living cell operate in a highly noisy environment. What are the specific …

We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing
species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic …

We study a tractable opinion dynamics model that generates long-run disagreements and
persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip …

A nonlinear Markov evolution is a dynamical system generated by a measure-valued
ordinary differential equation with the specific feature of preserving positivity. This feature …

Ecological systems are complex assemblies of large numbers of individuals, interacting
competitively under multifaceted environmental conditions. Recent studies using microbial …

Focusing on competitive Lotka–Volterra model in random environments, this paper uses
regime-switching diffusions to model the dynamics of the population sizes of n different …

This review provides a pedagogic and self-contained introduction to master equations and
to their representation by path integrals. Since the 1930s, master equations have served as …