The understanding of the evolution in biological systems can help us get some ideas in extracting biological mechanisms. The evolution process of biological systems usually involves the propagation of the waves. Hence it seems to be necessary to study these biological wave patterns. In this mini-course, we will introduce some theoretical tools to study these wave patterns, and then apply these methods to some biological models.

 

The following topics will be covered:

(1) Wave theory for monotone semiflows in the monostable case;

(2) Wave theory in reaction-diffusion equations.