This is the final project I worked on for PHYS304 Computational Physics with Professor Daniel Grin at Haverford College in Spring 2020 semester. This project studied two Chaotic systems, both of which are governed by a system of 2nd order differential equations: Damped Driven Pendulum System and Henon-Heiles systems. This work made use of odeint from scipy.integrate to find the numerical solutions. I also explored different plots for visualizations, and paid a great focus on Poincare scetions and Bifurcation diagrams.
Here is a breakdown of the files in this repository:
- xia_final_Chaotic_Systems.pdf: a write-up for this final project
- DDP: contains all files related to sutdying DDP systems
- xia_DDP.py: the behavior of DDP systems with different parameters
- xia_InitialCond.py: for comparing identical systems under different initial conditions
- xia_Bifurcate.py: for generating bifurcation diagram and finding the critical values of bifurcation points
- xia_animate_plot.py: a simple animation that shows the time-evolution of the system
- HenonHeiles:
- xia_HenonHeiles.py: solve and produce 3D phase plots of Henon-Heiles systems under different inital conditions.
- xia_Poincare.py: generate the Poincare sections of the system under different initial conditions