Patterns are ubiquitous in living systems and underlie the dynamic organization of cells,
tissues, and embryos. Mathematical frameworks have been devised to account for the self …

One of the major challenges in modern biology is to understand how the molecular
components of a living cell operate in a highly noisy environment. What are the specific …

Biological and biochemical systems are manifestations of chemical reaction networks
(CRNs). The ability to design and engineer such networks may allow the construction of …

The formation of repetitive structures (such as stripes) in nature is often consistent with a
reaction-diffusion mechanism, or Turing model, of self-organizing systems. We used mouse …

In this work, the solution of Riesz space fractional partial differential equations of parabolic
type is considered. Since fractional-in-space operators have been applied to model …

Many chemical systems exhibit a range of patterns, a noticeable and interesting class of
numerical patterns that arise in autocatalytic reactions which changes with increasing spatial …

Time-dependent advection–diffusion–reaction and diffusion–reaction equations are used as
models in biology, chemistry, physics, and engineering. As representative examples, we …

We present a contribution to the field of system identification of partial differential equations
(PDEs), with emphasis on discerning between competing mathematical models of pattern …

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

This paper deals with the effects of partial differential equations on the development of
spatiotemporal patterns in reaction–diffusion systems. These systems describe how the …