Periodic travelling waves have been reported in a number of recent spatio-temporal field
studies of populations undergoing multi-year cycles. Mathematical modelling has a major …

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 …

In this paper we introduce a conceptual model for vegetation patterns that generalizes the
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …

Spatial patterns at the landscape scale have been documented in a wide variety of
ecosystems across many parts of the world. Mathematical models have played an important …

We consider predator invasions for the nonlocal Holling–Tanner model. Predators are
introduced in a small region adjacent to an extensive predator-free region. In its simplest …

Motivated by the impact of worsening climate conditions on vegetation patches, we study
dynamic instabilities in an idealised Ginzburg–Landau model. Our main results predict time …

We consider the evolution of multi-pulse patterns in an extended Klausmeier equation with
parameters that change in time and/or space. We formally show that the full PDE dynamics …

The savanna biome is characterised by a continuous vegetation cover, comprised of
herbaceous and woody plants. The coexistence of species in arid savannas, where water …

Pattern formation is the sub-area of complexity science in which the dynamics of nonlinear
spatial processes is studied. Reaction-diffusion systems appear as relevant models for such …

A variety of numerical methods are available for determining the stability of a given solution
of a partial differential equation. However for a family of solutions, calculation of boundaries …