Spontaneous pattern formation is a fundamental scientific problem that has received much
attention since the seminal theoretical work of Turing on reaction-diffusion systems. In …

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

The advances in understanding complex networks have generated increasing interest in
dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has …

Pattern formation from homogeneity is well studied, but less is known concerning symmetry-
breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial …

Models for self-organization have been used in complex systems across numerous
disciplines, with a prime example given by the Turing instability. However, this instability is …

We show that a model reaction-diffusion system with two species in a monostable regime
and over a large region of parameter space produces Turing patterns coexisting with a limit …

Networks have become ubiquitous in the modern scientific literature, with recent work
directed at understanding 'temporal networks'—those networks having structure or topology …

It is well known that simple reaction–diffusion systems can display very rich pattern formation
behaviour. Here we have studied two examples of such systems in three dimensions. First …

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 …

Reactive lattice gas automata simulations show that Turing structure can form on a
mesoscopic scale and are stable to molecular fluctuations in this domain. Calculations on …