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Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can…
We discuss the role of spatial correlations of the noise in the array enhanced stochastic resonance. We show numerically that the noises with negative correlations between different sites lead to significantly larger values of the…
Territorial behaviour is widespread in the animal kingdom, with creatures seeking to gain parts of space for their exclusive use. It arises through a complicated interplay of many different behavioural features. Extracting and quantifying…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
A dynamical system of equations describing parametric sound generation (PSG) in a dispersive large aspect ratio resonator is derived. The model generalizes previously proposed descriptions of PSG by including diffraction effects, and is…
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous…
In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…
Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement…
We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single and where several predators compete with each other. In this…
In this paper we investigate a free boundary problem for a predator-prey model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We present measurements on parametrically driven surface waves (Faraday waves) performed in the vicinity of a bi-critical point in parameter space, where modes with harmonic and subharmonic time dependence interact. The primary patterns are…
The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal…
Although spatial prediction is widely used for urban and environmental monitoring, its accuracy is often unsatisfactory if only a small number of samples are available in the study area. The objective of this study was to improve the…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…