Related papers: Spatio-temporal Moran dynamics in continuous media
In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
We propose a model to study the spatiotemporal dynamics of biocrust and vegetation cover on sand dunes. The model consists of two coupled partial nonlinear differential equations and includes diffusion and advection terms for modeling the…
We identify two pathological cases of temporal inconsistencies in video generation: video freezing and video looping. To better quantify the temporal diversity, we propose a class of complementary metrics that are effective, easy to…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
In general, space-time wave packets with correlations between transverse spatial fields and temporal frequency spectra can lead to unique spatiotemporal dynamics, thus enabling control of the instantaneous light properties. However,…
Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data…
Broom and Rycht\'{a}\v{r} [Proc. R. Soc. A (2008) 464, 2609--2627] found an exact solution for the fixation probabilities of the Moran process for a structured population, in which the interaction structure among individuals is given by the…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
This paper is devoted to the study of spatial propagation dynamics of species in locally spatially inhomogeneous patchy environments or media. For a lattice differential equation with monostable nonlinearity in a discrete homogeneous media,…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
Materials adsorbed to the surface of a fluid -- for instance, crude oil, biogenic slicks, or industrial/medical surfactants -- will move in response to surface waves. Due to the difficulty of non-invasive measurement of the spatial…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…
We discuss the dynamics of zonal (or unidirectional) jets for barotropic flows forced by Gaussian stochastic fields with white in time correlation functions. This problem contains the stochastic dynamics of 2D Navier-Stokes equation as a…
Starting from an age-structured diffusive population growth law for single species in a discrete and periodic habitat, we formulate a stage structured population model with spatially periodic dispersal, mortality and recruitment. With a KPP…