In this review, we provide a concise summary of several important mathematical results for
stochastic travelling waves generated by monostable and bistable reaction-diffusion …

We develop numerical methods for stochastic reaction-diffusion systems based on
approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD …

Cell polarization is an important part of the response of eukaryotic cells to stimuli, and forms
a primary step in cell motility, differentiation, and many cellular functions. Among the …

The position of propagating population fronts fluctuates because of the discreteness of the
individuals and stochastic character of processes of birth, death, and migration. Here we …

The process of desertification is usually modeled as a first-order transition, where a change
of an external parameter (eg, precipitation) leads to a catastrophic bifurcation followed by an …

We consider the spread of epidemic in a spatial metapopulation system consisting of weakly
interacting patches. Each local patch is represented by a network with a certain node degree …

Continuum models of epidemics do not take into account the underlying microscopic
network structure of social connections. This drawback becomes extreme during quarantine …

Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an
obvious focus on average stresses in a continuum mechanical approximation. However …

We investigate phase coexistence in a weakly stochastic reaction-diffusion system without
assuming a continuum description. Concretely, for $(2N+ 1) $ diffusion-coupled vessels in …

Spreading cell fronts play an essential role in many physiological processes. Classically,
models of this process are based on the Fisher–Kolmogorov equation; however, such …