Periodic travelling waves (wavetrains) are an important solution type for many partial
differential equations. In this paper I review the use of numerical continuation for studying …

This study presents a novel unsupervised convolutional Neural Network (NN) architecture
with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal …

Mechanisms and scenarios of pattern formation in predator–prey systems have been a focus
of many studies recently as they are thought to mimic the processes of ecological patterning …

Mathematical models have been highly successful at reproducing the complex
spatiotemporal phenomena seen in many biological systems. However, the ability to …

The paper presents an adapted numerical integration for advection–reaction–diffusion
problems. The numerical scheme, exploiting the a-priori knowledge of the qualitative …

Banded vegetation is a characteristic feature of semiarid environments, comprising stripes of
vegetation running parallel to the contours on hillsides, separated by stripes of bare ground …

The numerical solution of reaction–diffusion equations of λ–ω type, which are known to
possess a one-parameter family of periodic plane wave solutions, is object of this paper …

Banded vegetation is a characteristic feature of semi-arid environments. It occurs on gentle
slopes, with alternating stripes of vegetation and bare ground running parallel to the …

We describe simple finite element schemes for approximating spatially extended predator–
prey dynamics with the Holling type II functional response and logistic growth of the prey …

We consider the selection and stability of periodic wave trains that form behind invasion
fronts in predator–prey reaction–diffusion models where the prey compete in a non-local …