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New algorithm for detection of UPOs #328

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merged 11 commits into from
Mar 26, 2024

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JonasKoziorek
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Hi!

I have added Davidchack-Lai algorithm for detection of unstable periodic orbits: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.60.6172
https://www.sciencedirect.com/science/article/pii/S0375960101004637

I have included docstring and tests. I have also wrote examples for documentation, however I don't know how to create the documentation website locally, so I haven't seen the output. When I run /docs/make.jl it results in an error even without my additions.

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codecov-commenter commented Mar 20, 2024

Codecov Report

Attention: Patch coverage is 92.92035% with 8 lines in your changes are missing coverage. Please review.

Project coverage is 61.10%. Comparing base (928bdb0) to head (4a19099).
Report is 6 commits behind head on main.

Files Patch % Lines
src/periodicity/davidchacklai.jl 95.34% 4 Missing ⚠️
src/periodicity/lambdamatrix.jl 84.00% 4 Missing ⚠️
Additional details and impacted files
@@            Coverage Diff             @@
##             main     #328      +/-   ##
==========================================
+ Coverage   54.86%   61.10%   +6.23%     
==========================================
  Files          22       25       +3     
  Lines         904     1036     +132     
==========================================
+ Hits          496      633     +137     
+ Misses        408      403       -5     

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@Datseris
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I'll fix the docs in this PR and then review...

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This is good for now, i only have minor comments. In the future we could combine things more into a single function periodicorbits where a special type is used to dispatch on the algorithm.

The main difference between Schmelcher & Diakonos[^Schmelcher1997] and
Davidchack & Lai[^Davidchack1999] is that the latter uses periodic points of
previous period as seeds to detect periodic points of the next period.
Additionally, `periodicorbits` only detects periodic points of a given order,
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When you are referring to a function wrap it in an @ref decorator;

[`periodicorbit`](@ref) 

davidchacklai(ds::DeterministicIteratedMap, n::Int, ics, m::Int; kwargs...) -> fps

Find periodic orbits `fps` of orders `1` to `n` for the map `ds`
using the algorithm propesed by Davidchack & Lai[^Davidchack1999].
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LEt's prepare ourselves for using documenter citations.

Create a new file docs/refs.bib. Add there the BiBtex entry for DavidCha1999. Cite it using

[DavidChack1999](@cite) 

and in the docs/make.jl uncomment the corresponding Bibliography related code.

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I am merging this in, we don't have a changelog entry yet, but you mentioned you will do this in a different PR!

@Datseris Datseris merged commit 1c424f7 into JuliaDynamics:main Mar 26, 2024
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3 participants