Colloquium Mathematics - D. van Kekem (PhD Student)

Title:

Dynamics of the Lorenz-96 model

Abstract:

The Lorenz-96 model is, due to its simplicity, widely used as a test model for various applications, such as data assimilation methods. This symmetric model contains $\Integer_n$-symmetry and has as free parameters the forcing $F\in\Real$ and the dimension of the state space $n\in\Nat$. We explored the dynamics of the monoscale Lorenz-96 model for both positive and negative $F$ using both analytical and numerical means.

In this talk, we show that different types of waves can arise the Lorenz-96 model, depending on the dimension $n$ and the sign of $F$. We present the pattern that comprises all possible bifurcation routes from a single stable equilibrium to one or more stable waves. Finally, we discuss the occurrence of two or more coexisting stable waves through multiple double-Hopf bifurcations or via multiple pitchfork bifurcations.