This repository contains a collection of programs and analyses related to the study of (non)linear dynamical systems, developed as part of the coursework in the Master's programme in Applied Physics (specialization: Computational Physics). The projects cover fundamental topics in dynamical systems theory, including ODE/PDE, phase–space analysis, bifurcations, and chaotic behavior. List of projects:
- Introduction to the GSL library
- Stability of fixed points in ODEs
- Simple pendulum and phase portraits
- Orbits and polar coordinates
- Bifurcations
- The van der Pol oscillator
- Bifurcation diagrams and the Lyapunov exponent
- The atomic kicked rotator and Poincaré sections
- Hénon map, fractal dimensions
- Logistic map, multifractal dimensions
The GIF below shows the evolution of the Poincaré section of the standard (Chirikov–Taylor) map as the parameter (K) increases.
Multiple trajectories with different initial momentum values are iterated to visualize how the phase–space structure transitions from regular motion to widespread chaos.
All mathematical details and derivations are included in the report located in the lab_8 folder
