Based on first principles, we derive a general model to describe the spatio-temporal
dynamics of two morphogens. The diffusive part of the model incorporates the dynamics …

Many problems in biology involve growth. In numerical simulations it can therefore be very
convenient to employ a moving computational grid on a continuously deforming domain. In …

Reaction-diffusion systems have been widely studied in developmental biology, chemistry
and more recently in financial mathematics. Most of these systems comprise nonlinear …

Nonlinear reaction-diffusion systems which are often employed in mathematical modeling in
developmental biology are usually highly stiff in both diffusion and reaction terms. Moreover …

The pattern formation in reaction–diffusion system has long been the subject of interest to
the researchers in the domain of mathematical ecology because of its universal existence …

Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated
multicellular organisms, exhibit a property referred to as symmetry. However, precise …

The significant and meaningful fraction of all the potential information residing in the
molecules and structures of living systems is unknown. Sets of random molecular …

Reaction-diffusion systems have been widely used to model pattern formation in biological
systems. However, the emergence of Turing patterns in three-dimensional (3D) domains …

Nonlinear diffusion-reaction systems model a multitude of physical phenomena. A common
situation is biological development modeling where such systems have been widely used to …

It is well known that in two dimensions Turing systems produce spots, stripes and
labyrinthine patterns, and in three dimensions lamellar and spherical structures, or their …