Numerical analysis techniques for non-linear dynamics

TL;DR

This paper reviews numerical analysis techniques for non-linear dynamics, emphasizing phase space analysis, resonance behavior, chaos detection methods, and their applications to complex systems.

Contribution

It provides an overview of modern numerical methods for analyzing non-linear dynamical systems, including chaos detection and resonance analysis.

Findings

Frequency map analysis effectively detects chaos.

Non-linear effects significantly influence system stability.

Resonance phenomena are crucial in understanding system dynamics.

Abstract

The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of fixed points in their topology and dynamics, the motion close to a resonance is presented, with simple non-linear map examples. The onset of chaotic motion and the modern methods used for their detection are detailed with a focus on frequency map analysis and concrete examples for a variety of rings and non-linear effects.