In the nearly seven decades since the publication of Alan Turing's work on morphogenesis,
enormous progress has been made in understanding both the mathematical and biological …

The spontaneous emergence of patterns in nature, such as stripes and spots, can be
mathematically explained by reaction-diffusion systems. These patterns are often referred as …

First proposed by Turing in 1952, the eponymous Turing instability and Turing pattern
remain key tools for the modern study of diffusion-driven pattern formation. In spatially …

Reaction–diffusion systems are an intensively studied form of partial differential equation,
frequently used to produce spatially heterogeneous patterned states from homogeneous …

Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal
pattern formation are rarely isolated systems, either chemically or thermodynamically …

We study a mathematical model of invasion in the case of two closely related species. The
model is formulated as a system of nonlinear partial differential equations, which takes into …

Patterns, typical spatiotemporal ordered structures, are widely present in a variety of
systems, which are the results of the emergence of complex systems. The theory of Turing …

We study traveling waves in a non-local cross-diffusion-type model, where organisms move
along gradients in population densities. Such models are valuable for understanding waves …

Investigations are undertaken into simple predator–prey models with rational interaction
terms in one and two spatial dimensions. Focusing on a case with linear interaction and …

We develop an agent-based model on a lattice to investigate territorial development
motivated by markings such as graffiti, generalizing a previously-published model to account …