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Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions.…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
In this paper, we analyze the dynamics of an $N$ particles system evolving according the gradient flow of an energy functional. The particle system is a consistent approximation of the Lagrangian formulation of a one parameter family of…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…
Autocatalytic processes underlie diverse systems in which replication is triggered at interfaces, including heterogeneous catalysis on solid substrates, enzyme activity at membranes, viral infections, biofilm growth, and spatially…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…
Extinction is the ultimate absorbing state of any stochastic birth-death process, hence the time to extinction is an important characteristic of any natural population. Here we consider logistic and logistic-like systems under the combined…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…