Mathematical modelling of chemotaxis (the movement of biological cells or organisms in
response to chemical gradients) has developed into a large and diverse discipline, whose …

The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

When we contemplate phenomena as diverse as electrochemical deposition or the spatial
patterns of urban development, it is natural to assume that they havenothing incommon …

In nature, microorganisms must often cope with hostile environmental conditions. To do so
they have developed sophisticated cooperative behaviour and intricate communication …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for
attracting microbes to food, embryonic cells into developing tissues, immune cells to …

In this paper, we concern about a modified version of the Keller-Segel model. The Keller-
Segel is a system of partial differential equations used for modeling Chemotaxis in which …

A" brain defibrillator" may be closer than we think. An epileptic seizure involves a
paroxysmal change in the activity of millions of neurons. Feedback control of seizures would …

In vertebrate embryos, somites, the precursor of vertebrae, form from the presomitic
mesoderm (PSM), which is composed of cells displaying signaling oscillations. Cellular …

This paper is devoted mainly to the global existence problem for the two-dimensional
parabolic-parabolic Keller-Segel system in the full space. We derive a critical mass …