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We study a dynamical system modeling the Theory of Planned Behavior (TPB) in which each individual's behavioral intention evolves continuously under an ODE driven by internal attitudes, perceived social norms, and perceived behavioral…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
We introduce a class of distributed nonlinear control systems, termed as the flow-tracker dynamics, which capture phenomena where the average state is controlled by the average control input, with no individual agent has direct access to…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
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…
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
A simple queueing approach for segregation of agents in modified one dimensional Schelling segregation model is presented. The goal is to arrive at simple formula for the number of unhappy agents remaining after the segregation.
Linking the microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: while physical particles are assumed to optimize the global…
In the first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of nonspherical particles, within a parallelepiped simulation domain, under both periodic or…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
The goal of this work is to study an infectious disease spreading in a medium size population occupying a confined environment. For this purpose, we consider a kinetic theory approach to model crowd dynamics in bounded domains and couple it…
Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous…
The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to…