This folder contains a collection of useful Notebooks with tutorials on how to use the LDDS Lagrangian descriptors Python module for analyzing the phase space structure of dynamical systems.
Tutorial 1 Continuous 1DoF systems (no perturbation)
- Hamilton centre (autonomous)
- Hamilton saddle (autonomous)
- Duffing oscillator (autonomous)
- Double-gyre (nonautonomous)
Tutorial 2 Lagrangian descriptors for 1 DoF dynamical system with forcing
- Forced Duffing oscillator (nonautonomous)
Tutorial 3 Variable time integration
- Hamilton saddle-node
- Inverted Duffing oscillator
Tutorial 4 Lagrangian descriptors for a user-defined 1 DoF dynamical system
- Morse oscillator
Tutorial 5 High-dimensional continuous systems
- 2DoF Hénon-Heiles
- 2DoF Index-1 normal form saddle
- 3DoF index-1 normal form saddle
Tutorial 6 Lagrangian descriptors for a user-defined 2 DoF Hamiltonian
- Double-well Hamiltonian system
Tutorial 7 Dynamics using Potential Energy Surface (PES) data
- Discretised Hénon-Heiles
Tutorial 8 Lagrangian descriptors for maps of discrete systems
- Standard map
- Hénon map
Tutorial 9 User-defined discrete maps
- Gauss map
- Gingerbreadman map
Tutorial 10 Lagrangian descriptors for Stochastic Dynamical Systems
- Noisy saddle
- Noisy Duffing oscillator
- Noisy double-gyre
Tutorial 11 Dynamics using a vector field dataset
- Discretised forced Duffing oscillator
Tutorial 12 Integration Time & Grid Resolution for Lagrangian descriptor Simulations
- Arnold's cat map
- Double-gyre flow
More to come...
We encourage contributions from users to develop Jupyter notebooks that extend the capabilities and features of the LDDS software package.