Edgetracking algorithm

.gitignore

@@ -3,4 +3,5 @@ Manifest.toml
 *.scss
 *.css
 .vscode
-*style.jl
+*style.jl
+.DS_Store

Project.toml

@@ -2,7 +2,7 @@ name = "Attractors"
 uuid = "f3fd9213-ca85-4dba-9dfd-7fc91308fec7"
 authors = ["George Datseris <datseris.george@gmail.com>", "Kalel Rossi", "Alexandre Wagemakers"]
 repo = "https://github.com/JuliaDynamics/Attractors.jl.git"
-version = "1.13.5"
+version = "1.14.0"
 
 [deps]
 BlackBoxOptim = "a134a8b2-14d6-55f6-9291-3336d3ab0209"

docs/refs.bib

@@ -158,4 +158,65 @@ @article{Halekotte2020
  author = {Lukas Halekotte and Ulrike Feudel},
  title = {Minimal fatal shocks in multistable complex networks},
  journal = {Scientific Reports}
+}
+
+@article{Battelino1988,
+ title={Multiple coexisting attractors, basin boundaries and basic sets},
+ author={Battelino, Peter M and Grebogi, Celso and Ott, Edward and Yorke, James A and Yorke, Ellen D},
+ journal={Physica D: Nonlinear Phenomena},
+ volume={32},
+ number={2},
+ pages={296--305},
+ year={1988},
+ publisher={Elsevier}
+}
+
+@article{Skufca2006,
+ title={Edge of chaos in a parallel shear flow},
+ author={Skufca, Joseph D and Yorke, James A and Eckhardt, Bruno},
+ journal={Physical review letters},
+ volume={96},
+ number={17},
+ pages={174101},
+ year={2006},
+ publisher={APS}
+}
+
+@article{Schneider2008,
+ title={Laminar-turbulent boundary in plane Couette flow},
+ author={Schneider, Tobias M and Gibson, John F and Lagha, Maher and De Lillo, Filippo and Eckhardt, Bruno},
+ journal={Physical Review E},
+ volume={78},
+ number={3},
+ pages={037301},
+ year={2008},
+ publisher={APS}
+}
+
+@article{Wagemakers2020,
+ title={The saddle-straddle method to test for Wada basins},
+ author={Wagemakers, Alexandre and Daza, Alvar and Sanju{\'a}n, Miguel AF},
+ journal={Communications in Nonlinear Science and Numerical Simulation},
+ volume={84},
+ pages={105167},
+ year={2020},
+ publisher={Elsevier}
+}
+
+@article{Lucarini2017,
+ title={Edge states in the climate system: exploring global instabilities and critical transitions},
+ author={Lucarini, Valerio and B{\'o}dai, Tam{\'a}s},
+ journal={Nonlinearity},
+ volume={30},
+ number={7},
+ pages={R32},
+ year={2017},
+ publisher={IOP Publishing}
+}
+
+@article{Mehling2023,
+ title={Limits to predictability of the asymptotic state of the Atlantic Meridional Overturning Circulation in a conceptual climate model},
+ author={Mehling, Oliver and B{\"o}rner, Reyk and Lucarini, Valerio},
+ journal={arXiv preprint arXiv:2308.16251},
+ year={2023}
 }

docs/src/basins.md

@@ -29,6 +29,14 @@ basins_fractal_test
 uncertainty_exponent
 ```
 
+## Edge tracking and edge states
+The edge tracking algorithm allows to locate and construct so-called edge states (also referred to as *Melancholia states*) embedded in the basin boundary separating different basins of attraction. These could be saddle points, unstable periodic orbits or chaotic saddles. The general idea is that these sets can be found because they act as attractors when restricting to the basin boundary.
+
+```@docs
+edgetracking
+bisect_to_edge
+```
+
 ## Tipping points
 This page discusses functionality related with tipping points in dynamical systems with known rule. If instead you are interested in identifying tipping points in measured timeseries, have a look at [TransitionIndicators.jl](https://github.com/JuliaDynamics/TransitionIndicators.jl).
 

docs/src/index.md

@@ -10,9 +10,7 @@ using CairoMakie, Attractors
 
 ## Latest news
 
-- Our paper on the global stability analysis framework offered by Attractors.jl ([`continuation`](@ref)) and the novel continuation offered by [`RecurrencesFindAndMatch`](@ref) is published as a _Featured Article_ in Chaos (https://pubs.aip.org/aip/cha/article/33/7/073151/2904709/Framework-for-global-stability-analysis-of) and has been featured in the AIP publishing showcase (https://www.growkudos.com/publications/10.1063%25252F5.0159675/reader)
-- New function [`minimal_fatal_shock`](@ref)
-- New function [`match_continuation!`](@ref) which improves the matching during a continuation process where attractors disappear and reappear.
+- New functions [`edgetracking`](@ref) and [`bisect_to_edge`](@ref) added that implement the **edge tracking algorithm**, a method to find saddles, *edge states* or *Melancholia states* in dynamical systems, also when they are unstable chaotic sets.
 
 ## Outline of Attractors.jl
 

src/Attractors.jl

@@ -18,6 +18,7 @@ include("dict_utils.jl")
 include("mapping/attractor_mapping.jl")
 include("basins/basins.jl")
 include("continuation/basins_fractions_continuation_api.jl")
+include("boundaries/edgetracking.jl")
 include("deprecated.jl")
 include("tipping/tipping.jl")