Chemotaxis and pattern formation in predator-prey models

The Rosenzweig-MacArthur predator-prey model, was  extended to include the prey's defense mechanism of escaping against the concentration gradient of a chemical signaling the presence of a predator (odor trace). Various variants of the model, which is a system of quasilinear parabolic equations, lead to interesting properties of solutions, some of which can be described by the bifurcation theory, while others indicate the formation of singular solutions in finite time. Numerical solutions  show a variety of spatio-temporal patterns.