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We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action…
We here discuss a model of continuous opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. We concentrate on the version of the…
We demonstrate how niche theory and Hubbell's original formulation of neutral theory can be blended together into a general framework modeling the combined effects of selection, drift, speciation, and dispersal on community dynamics. This…
We show that diversity, in the form of quenched noise, can have a constructive effect in the dynamics of extended systems. We first consider a bistable $\phi^4$ model composed by many coupled units and show that the global response to an…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
In both natural and artificial studies, evolution is often seen as synonymous to natural selection. Individuals evolve under pressures set by environments that are either reset or do not carry over significant changes from previous…
We discuss a crowd-based theory for describing the collective behavior in Complex Systems comprising multi-agent populations competing for a limited resource. These systems -- whose binary versions we refer to as B-A-R (Binary Agent…
Quenching and annealing are extreme opposites in the time evolution of a quantum system: Annealing explores equilibrium phases of a Hamiltonian with slowly changing parameters and can be exploited as a tool for solving complex optimization…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
We consider the dynamics imposed by natural selection on the populations of two competing, sexually reproducing, haploid species. In this setting, the fitness of any genome varies over time due to the changing population mix of the…
In recent years, opinion dynamics has received an increasing attention, and various models have been introduced and evaluated mainly by simulation. In this study, we introduce and study a dynamical model inspired by the so-called `bounded…
This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of…
For a binary choice problem, the spatial coordination of decisions in an agent community is investigated both analytically and by means of stochastic computer simulations. The individual decisions are based on different local information…
Polarization is a problem in modern society. Understanding how opinions evolve through social interactions is crucial for addressing conditions that lead to polarization, consensus, or opinion diversity. Classical opinion dynamics models…
One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become…
This paper introduces a model for opinion dynamics, where at each time step, randomly selected agents see their opinions - modeled as scalars in [0,1] - evolve depending on a local interaction function. In the classical Bounded Confidence…
A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…
We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced in PRE E 101, 012101 (2020) for the dynamics of voting intention. Each agent has a…