Nonlinear dynamics of coupled phase oscillators

Python package to study systems of coupled phase oscillators, for example

• Kuramoto model with local coupling on a two-dimensional lattice
• cilia carpet model (as studied in references [1, 2]; this example from biological physics gave this repository its name)
• new models can be added in a flexible manner

Features:

• define oscillator coupling and solve the corresponding equation of motion for the oscillator network (see examples below)
• visualize oscillator positions and phases
• useful routines for large-scale simulations (various.parallel_with_threads, various.logging)
• scripts: find fixed points, linear stability analysis, basins of attractions, etc.

The code can be applied to regular lattices as well as general networks of coupled phase oscillators.

How to use

• See examples
• General idea: import lattice type as import carpet.lattice.SOME_TYPE as lattice, import physics/coupling as import carpet.coupling.SOME_TYPE as coupling => define geometry and physics, define right_side_of_ODE Then use define_solve_cycle and dynamics can be integrated.

Installation

Run in terminal python setup.py develop.

• After that package is ready to be imported.
• Any changes to the code will be applied immediately.
• Package numba is optional, but highly recommended as it speeds up some computations (e.g., carpet.physics.friction_pairwise, carpet.physics.kuramoto_numpy).

Structure

• carpet - import it to get access to several modules, e.g.
  • dynamics
    • Functions to solve ODE
  • various:
    • logging for simulations
    • math functions
• Geometry-specific files (topology: chain, lattice, network?) are contained in packages inside lattice folder. Files contain functions to build a list of positions and connetions depending on the geometry of choice.
• Physics-specific files (how are oscillators coupled?): in physics folder.
  • Recommended use import carpet.physics.kuramoto as physics

Other modules should be imported separately, e.g., import carpet.visualize as vis.

• visualize - functions for visualization

• parallel_with_threads.py - code to run a function in parallel on a list of inputs.

• classes.py - implementation of oscillator classes; assume symmetry classes and reduce dimensionality of the ODE system.

• Many reusable functions reside outside the main package - these are located in folder scripts

Authors

• Anton Solovev
• Benjamin M. Friedrich, email: benjamin.m.friedrich@tu-dresden.de

Publication to cite: [2]

• [1]: Solovev & Friedrich 2021 EPJ E ST; also available as arXiv preprint
• [2]: Solovev & Friedrich 2020 arXiv:2012:11741