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 …

Today we can use physics to describe in great detail many of the phenomena intervening in
the process of life. But no analogous unified description exists for the phenomenon of life …

Turing theory of pattern formation is among the most popular theoretical means to account
for the variety of spatio-temporal structures observed in Nature and, for this reason, finds …

Spatial patterns through diffusion-driven instability are stationary structures that appear
spontaneously upon breaking the symmetry of the spatial domain, which results only from …

In this paper the formation of rhombic and hexagonal Turing patterns in bidimensional
hyperbolic reaction–transport systems is addressed in the context of dryland ecology. To this …

Chemical oscillators are open systems characterized by periodic variations of some reaction
species concentration due to complex physico-chemical phenomena that may cause …

In this paper, we consider a predator–prey model with herd behavior and cross-diffusion
subject to homogeneous Neumann boundary condition. Firstly, the existence and priori …

Hyperbolic reaction–diffusion equations have recently attracted attention both for their
application to a variety of biological and chemical phenomena, and for their distinct features …

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 …

In this paper, we investigate the phenomena of pattern formation for a predator–prey model
with herd behavior and cross-diffusion. We give the conditions for cross-diffusion induced …