This book presents several fundamental questions in mathematical biology such as Turing
instability pattern formation reaction-diffusion systems invasion waves and Fokker-Planck
equations. These are classical modeling tools for mathematical biology with applications to
ecology and population dynamics the neurosciences enzymatic reactions chemotaxis invasion
waves etc. The book presents these aspects from a mathematical perspective with the aim of
identifying those qualitative properties of the models that are relevant for biological
applications. To do so it uncovers the mechanisms at work behind Turing instability pattern
formation and invasion waves. This involves several mathematical tools such as stability and
instability analysis blow-up in finite time asymptotic methods and relative entropy
properties. Given the content presented the book is well suited as a textbook for master-level
coursework.
