Small changes in the initial state of the system can cause massive changes in the long run. This causes the analysis of said dynamical system significantly more difficult, which poses a problem, as situations of this sort arise in many fields of science. Nevertheless, we will find interesting results about the unexpected behaviour of Lorenz system. We will see at which parameters it behaves chaotically. Using the Hartman-Grobman theorem, we will linearize the system, making it easier to analyze locally. We will be using a Liapunov function to globally analyse the behaviour of solutions at certain parameters.
|
