[Re] Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations

2022 Replication of Glass and Sun (1994)

This project is a Julia 1.8.0 replication of Glass and Sun (1994), a paper that analyzed the global organization of phase locking zones of a periodically stimulated non-linear limit-cycle oscillator at various relaxation rates. Full reference to the original article:

L. Glass and J. Sun. “Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations.” In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Inter- disciplinary Topics; (United States) 50:6 (Dec. 1994). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.50.5077

Here we also include visual GIFs of the changing phase locking zones as a function of changing relaxation rate to the limit cycle:

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Authors

Jacob K. Harvey - Github, ORCID

Lucas Philipp - Github, ORCID

Kiri Stern - Github, ORCID

Running the code

Clone this repository to your own computer.

git clone https://github.com/jkharv/poincare_oscillator

cd into the directory and start a Julia REPL. This code is optimized for multiple threads, using the -t argument you can start Julia with multiple threads. Setting this to auto uses all available threads, otherwise set it to any integer value of threads you wish to use.

N.B. This script takes about 25-30 minutes to run when using 16 threads.

julia -t auto

To install the dependencies enter the package manager and enter the following commands,

] activate . 
instantiate

Then return from the package manager by hitting backspace.

Finally, run the code by sourcing the main script at the REPL.

include("src/poincare_oscillator.jl")