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We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…
Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…
Extracting the rules of real-world multi-agent behaviors is a current challenge in various scientific and engineering fields. Biological agents independently have limited observation and mechanical constraints; however, most of the…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state…
The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
We present experiments on the collective dynamics of macroscopic photoactive self-propelled particles subjected to spatiotemporally varying excitation. The particles move within an arena divided into two regions with different illumination…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
We present a practical method to generate classical trajectories with fixed initial and final boundary conditions. Our method is based on the minimization of a suitably defined discretized action. The method finds its most natural…
We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules.…