## Perturbations of the Lorenz system/Mathematical Physics

**Goal:**

The Lorenz system is a system of ordinary differential equations originally studied by Edward Lorenz in 1963 as a simple model of atmospheric convection. The system admits chaotic solutions for certain values of the parameters and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. In this project, you will investigate the Lorenz system and in particular, check the behaviour for various values of the parameters. After this, you can similarly investigate the behaviour of related systems including a periodically perturbed Lorenz system. One can search the vast literature for other examples or indeed propose your own modification of the system.

Alternatively, the project can be on a Physics phenomenon of the student's choosing. Relevant mathematical techniques will be considered.

**Schedule:** To be determined with the student(s).

**Supervisors:**
Andrew Bruce

**Difficulty level:**
Introductory/intermediate (some basic knowledge of differential equations is needed)

**Tools:**
A Mathematica notebook has been prepared for the students to modify. However, they would be free to use other computer languages if they wish.

**Results:**
To be completed at the end of the project.