Application of Dynamical Systems to Biology is nowadays an important challenge. In spite of profusion, convincing proof of chaotic dynamics in biological systems is usually difficult to make. However, in some application domains, chaotic indices can be used for diagnosis e.g. to classify the time series in two classes, such as healthy vs pathological. When one wants to describe evolution of chaotic systems, one usually need to solve an ODE or a PDE. The goal of this school is, on the one hand to present the basic tools in Dynamical Systems to solve ODE’s, and, on the second hand, to present how these tools can be used in Biology.
The school will comprise two series of three lectures. One theoretical one and one for applied mathematics. A large part will be devoted to exercises sessions.
The theoretical part will focus both on Symbolic Dynamics and Geometric Dynamics (mainly uniformly hyperbolic dynamical systems). Connections between the two aspects will be made (via the shadowing lemma and the construction of Markov partitions).
The applied part will make connections between the theoretical one by using the tools presented in the theoretical courses to study the logistic family, population evolution or emergence of epilepsy crises.
Deadline for registration and application: February 17, 2019.