Thomas Hillen – författare

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine.

The chapters of this book cover a wide range of mathematical methods and biological applications. They -       explain the process of mathematical modelling of biological systems with many examples, -       introduce advanced methods from dynamical systems theory, -       present many examples of the use of mathematical modelling to gain biological insight-       discuss innovative methods for the analysis of biological processes,-       contain extensive lists of references, which allow interested readers to continue the research on their own.

This beautifully crafted book collects images, which were created during the process of research in all fields of theoretical biology. Data analysis, numerical treatment of a model, or simulation results yield stunning images, which represent pieces of art just by themselves. The approach of the book is to present for each piece of visualization a lucid synopsis of the scientific background as well as an outline of the artistic vision. 

This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level.