Related papers: Intrinsic noise in structured replicator dynamics …
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and…
In genetic circuits, when the mRNA lifetime is short compared to the cell cycle, proteins are produced in geometrically-distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic…
We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a…
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
This paper is concerned with exploring the microscopic basis for the discrete versions of the standard replicator equation and the adjusted replicator equation. To this end, we introduce frequency-dependent selection -- as a result of…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
According to the standard imitation protocol, a less successful player adopts the strategy of the more successful one faithfully for future success. This is the cornerstone of evolutionary game theory that explores the vitality of competing…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
We analyse the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [1] reported that, while cooperation is sustained by perturbations…