Recognition of chaotic saddles through machine learning
Advisor
Habib Giuseppe
Email
habib@mm.bme.hu
Type
BSc MSc TDK
Language
hungarian english
Introduction:
Chaotic solutions are one of the most fascinating dynamical phenomena occurring in deterministic systems. Particularly interesting are the so-called chaotic saddles. These are unstable chaotic solutions, which have both attractive and repelling directions, which makes them saddles. They result in what is known as transient chaotic motions. In fact, a trajectory might be attracted by the chaotic saddle, but since the saddle is unstable, after a transient chaotic-like motion, the trajectory converges to a regular (non-chaotic) solution.The objective of this thesis is to understand basic phenomena recognizable in the vicinity of a chaotic saddle and to define a machine learning-based method to detect if a trajectory is passing near a chaotic saddle.
Tasks:
- study relevant literature about chaotic saddles- define two simple systems of interest presenting chaotic saddle
- perform a brief numerical analysis of the phenomena experienced when chaotic saddles are encountered
- define a neural network architecture (possible candidate: convolutional neural network) and test its capabilities in recognizing trajectories passing close to - chaotic saddles
- draw conclusions from the obtained results and summarize them
Artistic representation of a chaotic attractor
