README.md

BasinsCollection

This is a collection of multistable systems with the code to simulate their basins of attraction. Each file can be executed independently or there is a file called 'produce_basins.jl' to compute all the basins. This may take several days for some basins so be warned. Anyway, most basins will compute in some minutes for a 1200x1200 resolution.

The code is under MIT License, please cite the this repository or the companion article to this repo:

https://arxiv.org/abs/2504.01580

Alexandre Wagemakers

To (locally) reproduce this project, do the following:

0. Download this code base. Notice that raw data are typically not included in the git-history and may need to be downloaded independently.
1. Open a Julia console and do:

   julia> using Pkg
   julia> Pkg.add(DrWatson) # install globally, for using `quickactivate`
   julia> Pkg.activate(path/to/this/project)
   julia> Pkg.instantiate()
   

This will install all necessary packages for you to be able to run the scripts and everything should work out of the box, including correctly finding local paths.

Content:

• Basins for the Newton root finding algorithm

  

• Riddled basins ott_basins.jl: https://doi.org/10.1016/0167-2789(94)90047-7

  

• Riddled Basins from sommerer_basins.jl: Sommerer, John C. "The end of classical determinism." Johns Hopkins APL Technical Digest 16.4 (1995): 333.

  

• Duffing oscillator basins duffing_basins.jl

  

• Forced pendulum basins pendulum_basins.jl

  

• Hénon map map_henon.jl: https://doi.org/10.1016/j.physrep.2014.02.007

  

• Henon Heiles open Hamiltonian escape basins cuencas_hh.jl

  

• 4D kicked map rotor (1998) 4d_kicked.jl: https://doi.org/10.1016/S0960-0779(97)00058-1

  

• A map with hundred of attractors: kicked_rotor.jl: https://doi.org/10.1103/PhysRevE.54.71

  

• 4D kicked map rotor from kicked_ott.jl: https://doi.org/10.1016/0167-2789(87)90108-4

  

• A map with Wada map_feudel.jl: https://doi.org/10.1103/PhysRevE.58.3060

  

• Map with fractal boundary map_grebogi.jl: https://doi.org/10.1016/0375-9601(83)90945-3

  

• Fractal boundary in the josephson junction josephson_junction.jl: https://doi.org/10.1103/PhysRevA.36.2455

  

• Fractal Boundary from the magnetic pendulum magnetic_pendulum.jl: https://doi.org/10.1103/PhysRevLett.111.194101

  

• Rikitake oscillator basins rikitake.jl, unpublished.

  

• Thomas cyclical oscillator basins thomas.jl, unpublished

  

• Kuramoto oscillators on the UK power grid kur_halekotte.jl: https://doi.org/10.1088/2632-072X/ac080f

  

• Lorenz 84 system lorenz84.jl: https://doi.org/10.1063/1.2953589

  

• Slim fractals slim_fractals.jl: https://doi.org/10.1103/PhysRevX.7.021040

  

• Sporadical map sporadical_map.jl: https://doi.org/10.1103/PhysRevLett.82.3597

  

• Cold atoms cold_atoms.jl: https://doi.org/10.1103/PhysRevA.95.013629

  

• Competition ecology plancton competition_ecology_plancton.jl: https://doi.org/10.1086/319929

  

• Open Sinai billiard open_billiard_sinai.jl: https://doi.org/10.1103/PhysRevA.38.930

  

• Aguirre billiard aguirre_billiard.jl: https://doi.org/10.1103/PhysRevE.67.056201

  

• Poon billiard poon_billiard.jl: https://doi.org/10.1142/S0218127496000035

  

• Hidden attractors in Chua oscillators hidden_chua.jl: https://doi.org/10.1016/j.physleta.2011.04.037

  

• Li Sprott oscillator li_sprott.jl: https://doi.org/10.1142/S0218127416502333

  

• Binary Black Holes escape basins black_holes.jl: https://doi.org/10.1103/PhysRevD.98.084050

  

• Discrete predator Prey system predator_prey_discrete.jl: https://doi.org/10.1016/j.chaos.2022.112833

  

• Disipative nontwist map dsnm.jl: https://doi.org/10.1103/PhysRevE.107.024216

  

• 6D Shear Flow model lebovitz_mariotti.jl: https://doi.org/10.1017/jfm.2013.38

  

• 9D model of Fluid dynamics eckhardt_9D.jl: https://doi.org/10.1088/1367-2630/6/1/056 and https://doi.org/10.1103/PhysRevE.91.052903 (this last paper has a basins that I cannot reproduce)

  

• Wada basins in the cubic 2D map (map_cbic.jl): http://dx.doi.org/10.1016/j.physleta.2013.03.027

  

• Riddled basins of discrete 2D system map_kapitaniak.jl: https://doi.org/10.1103/PhysRevE.57.R6253

  

• Coupled logistic maps with riddled basins (Fig 15 of the paper has an error) map_cpled_logstc.jl: https://doi.org/10.1103/PhysRevE.57.2713

  

• Sprott-memristor model sprott_memristive.jl: https://doi.org/10.1016/j.chaos.2022.111834

  

• Parametrically forced pendulum para_pendulum.jl: http://dx.doi.org/10.1142/S0218127411030167

  

• Bogdanov map map_bogdanov.jl: https://doi.org/10.1142/S021812749300074X

  

• Coupled Lorenz systems coupled_lorenz.jl: https://doi.org/10.1103/PhysRevE.96.062203

  

• Rock-Paper-Scisors competition model cyclic_competition.j: https://doi.org/10.1063/1.5045366

  

• Split Ring Resonator model split_ring_resonator.jl: https://doi.org/10.1063/5.0157489

  

• Alfven Complexity alfven_complexity.jl: https://doi.org/10.1142/S0218127402005303

  

• Pump modulation erbium doped fiber laser (basins are slightly different) pumped_laser_dynamics.jl: https://doi.org/10.1016/j.physleta.2009.10.061

  

• CO2 modulated laser model (the basins in the paper are wrong due to numerical instabilities in the model) co2_modulated_laser.jl: https://doi.org/10.1063/5.0093727

  

• Threshold-Linear Networks with multistable patterns TLNs_network.jl: https://doi.org/10.1371/journal.pone.0264456

  

• Basins with tentacles kuramoto_basins_with_tentacles.jl: https://doi.org/10.1103/PhysRevLett.127.194101

  

• Riddled basins in coupled cuadratic map map_ashwin.jl: https://doi.org/10.1088/0951-7715/9/3/006

  

• Active Photonic Couplers photonic_coupler.jl: https://doi.org/10.1103/PhysRevA.100.043834

  

• Multistable Chimera in reduced Kuramoto model (two coupled populations) chimera_reduced_model.jl: https://doi.org/10.1088/1367-2630/18/2/022002

  

• Carpet oscillator carpet_oscillator.jl: https://doi.org/10.1007/s12043-018-1581-6

  

• Megastability: nested attractors: megastability_sprott.jl: https://doi.org/10.1140/epjst/e2017-70037-1

  

• Matryoshka multistability: matryoshka.jl: https://doi.org/10.1016/j.chaos.2024.115412

  

• Bairstow application: map_bairstow.jl: https://doi.org/10.1063/1.166158

  

• Quadratic map for basin bifurcations: map_mira.jl: https://doi.org/10.1142/S0218127494000241

  

• Geographic Economic competition model: economic_geographic_model.jl: http://dx.doi.org/10.1016/j.matcom.2014.01.004

  

• Multistability in a dynamic Cournot game: map_nash_eq.jl:

  

• Nonsmooth models of gear rattle oscilator: gear_rattle.jl: https://doi.org/10.1142/S021812740902283X

  

• Piecewise Smooth Dynamical System: map_lai.jl: https://doi.org/10.1063/1.2985853

  

• Basin bifurcations in quasiperiodically forced coupled systems: map_shrimali.jl: https://doi.org/10.1103/PhysRevE.72.036215

  

• Basins of attraction in a gear ratlle oscillator: gear_rattle_souza.jl: https://doi.org/10.1177/107754630100700605

  

• Basins of attraction of different ringing schemes of the church bell: bell_yoke2.jl: https://doi.org/10.1016/j.ijimpeng.2015.06.008

  

• Basins of a multiply regulated biochemical system: decroly_biorhythm.jl: https://doi.org/10.1073/pnas.79.22.6917

  

• Multistability in discrete chaotic systems using numerical integration with variable symmetry: map_vcsd_chen.jl: https://doi.org/10.1016/j.chaos.2022.112794

  

• Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins: neuron_synapse.jl: https://doi.org/10.1063/5.0125611

  

• Grazing chaos in impacting system: souza_impacting.jl: https://doi.org/10.1016/j.chaos.2007.01.022

  

• Simplified discretized Lorenz model: lorenz_computational_chaos.jl: https://doi.org/10.1016/0167-2789(89)90072-9

  

• Cournot economic game in 2D: map_bischi_cournot.jl: https://doi.org/10.1016/S0960-0779(98)00130-1

  

• Chaotic Gyrostat basins: gyrostat.jl: https://doi.org/10.3390/math10111914

  

• Intermingled basins in a triangular map: map_intermingled.jl: https://doi.org/10.1017/S0143385700009020,

  

• Ricker-Gatto competition model: map_ricker_gatto.jl: https://doi.org/10.1016/S0960-0779(00)00047-3

  

• Dynamics of random neural networks with bistable units: multistable_rand_net.jl https://doi.org/10.1103/PhysRevE.90.062710

  

• Earth magnetic field reversal model: earth_field_reversal.jl https://10.1140/epjb/e2012-20799-5