add strange attractor examples

Author: anandijain

Project.toml

@@ -7,6 +7,7 @@ version = "4.13.2"
 Catalyst = "479239e8-5488-4da2-87a7-35f2df7eef83"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 DiffEqOperators = "9fdde737-9c7f-55bf-ade8-46b3f136cc48"
+Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"

src/DiffEqProblemLibrary.jl

@@ -1,6 +1,7 @@
 module DiffEqProblemLibrary
 
 module ODEProblemLibrary
+using Latexify
 function importodeproblems()
   @isdefined(prob_ode_linear) ||
   include(joinpath(@__DIR__, "ode/ode_premade_problems.jl"));

src/ode/ode_premade_problems.jl

@@ -5,17 +5,22 @@ Random.seed!(100)
 
 #ODE Example Problems
 export prob_ode_linear, prob_ode_bigfloatlinear, prob_ode_2Dlinear,
-       prob_ode_large2Dlinear, prob_ode_bigfloat2Dlinear, prob_ode_rigidbody,
-       prob_ode_2Dlinear_notinplace, prob_ode_vanderpol, prob_ode_vanderpol_stiff,
-       prob_ode_lorenz, prob_ode_rober, prob_ode_threebody, prob_ode_mm_linear, prob_ode_pleiades,
-       prob_ode_brusselator_1d, prob_ode_brusselator_2d, prob_ode_orego,
-       prob_ode_hires, prob_ode_pollution, prob_ode_filament,
-       prob_ode_nonlinchem,
-       SolverDiffEq, filament_prob
+        prob_ode_large2Dlinear, prob_ode_bigfloat2Dlinear, prob_ode_rigidbody,
+        prob_ode_2Dlinear_notinplace, prob_ode_vanderpol, prob_ode_vanderpol_stiff,
+        prob_ode_rober, prob_ode_threebody, prob_ode_mm_linear, prob_ode_pleiades,
+        prob_ode_brusselator_1d, prob_ode_brusselator_2d, prob_ode_orego,
+        prob_ode_hires, prob_ode_pollution, prob_ode_filament,
+        prob_ode_nonlinchem,
+        SolverDiffEq, filament_prob,
+        thomas, lorenz, aizawa, dadras, chen, rossler, rabinovich_fabrikant, sprott, hindmarsh_rose,
+        prob_ode_thomas, prob_ode_lorenz, prob_ode_aizawa, prob_ode_dadras, 
+        prob_ode_chen, prob_ode_rossler, prob_ode_rabinovich_fabrikant, prob_ode_sprott,
+        prob_ode_hindmarsh_rose
 
 include("ode_linear_prob.jl")
 include("ode_simple_nonlinear_prob.jl")
 include("brusselator_prob.jl")
 include("pollution_prob.jl")
 include("filament_prob.jl")
 include("nonlinchem.jl")
+include("strange_attractors.jl")

src/ode/ode_simple_nonlinear_prob.jl

@@ -87,7 +87,7 @@ with ``μ=10^6`` and ``u_0=[0,\\sqrt{3}]``
 
 Stiff parameters.
 """
-prob_ode_vanstiff = ODEProblem(van,[0;sqrt(3)],(0.0,1.0),1e6)
+prob_ode_vanderpol_stiff = ODEProblem(van,[0;sqrt(3)],(0.0,1.0),1e6)
 
 # ROBER
 @parameters t k₁ k₂ k₃

src/ode/strange_attractors.jl

@@ -0,0 +1,221 @@
+# Strange attractors from https://www.dynamicmath.xyz/strange-attractors/ and
+# https://en.wikipedia.org/wiki/List_of_chaotic_maps
+# Opted for the equations as reported in papers 
+
+# Thomas
+@parameters t b=0.208186
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ sin(y) - b*x,
+       D(y) ~ sin(z) - b*y,
+       D(z) ~ sin(x) - b*z]
+
+@named thomas = ODESystem(eqs)
+
+"""
+Thomas' cyclically symmetric attractor equations
+
+```math
+$(latexify(thomas))
+```
+
+[Reference](https://www.worldscientific.com/doi/abs/10.1142/S0218127499001383)
+
+[Wikipedia](https://en.wikipedia.org/wiki/Thomas%27_cyclically_symmetric_attractor)
+"""
+prob_ode_thomas= ODEProblem(thomas,[],(0.0,1.0))
+
+
+# Lorenz
+@parameters t σ=10 ρ=28 β=8/3
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ σ*(y-x),
+       D(y) ~ x*(ρ-z)-y,
+       D(z) ~ x*y - β*z]
+
+@named lorenz = ODESystem(eqs)
+
+"""
+Lorenz equations
+
+```math
+$(latexify(lorenz))
+```
+
+[Reference](https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml)
+
+[Wikipedia](https://en.wikipedia.org/wiki/Lorenz_system)
+"""
+prob_ode_lorenz = ODEProblem(lorenz,[],(0.0,1.0))
+
+
+# Aizawa
+@parameters t a=0.95 b=0.7 c=0.6 d=3.5 e=0.25 f=0.1
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ (z-b)*x-d*y,
+       D(y) ~ d*x+(z-b)*y,
+       D(z) ~ c+a*z-z^3/3-(x^2+y^2)*(1+e*z)+ f*z*x^3]
+
+@named aizawa = ODESystem(eqs)
+
+"""
+Aizawa equations
+
+```math
+$(latexify(aizawa))
+```
+
+[Reference](https://journals.ametsoc.org/view/journals/atsc/20/2/1520-0469_1963_020_0130_dnf_2_0_co_2.xml)
+
+"""
+prob_ode_aizawa = ODEProblem(aizawa,[],(0.0,1.0))
+
+
+# Dadras
+@parameters t a=3 b=2.7 c=1.7 d=2 e=9
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ y-a*x+b*y*z,
+       D(y) ~ c*y-x*z+z,
+       D(z) ~ d*x*y-e*z]
+
+@named dadras = ODESystem(eqs)
+
+"""
+Dadras equations
+
+```math
+$(latexify(dadras))
+```
+
+[Reference](https://www.sciencedirect.com/science/article/abs/pii/S0375960109009591)
+
+"""
+prob_ode_dadras = ODEProblem(dadras,[],(0.0,1.0))
+
+
+# chen
+@parameters t a=35 b=3 c=28
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ a*(y-x),
+       D(y) ~ (c-a)*x-x*z+c*y,
+       D(z) ~ x*y-b*z]
+
+@named chen = ODESystem(eqs)
+
+"""
+chen equations
+
+```math
+$(latexify(chen))
+```
+
+[Reference](https://www.worldscientific.com/doi/abs/10.1142/S0218127499001024)
+
+"""
+prob_ode_chen = ODEProblem(chen,[],(0.0,1.0))
+
+
+# rossler
+@parameters t a=0.2 b=0.2 c=5.7
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ -(y+z),
+       D(y) ~ x+a*y,
+       D(z) ~ b+z*(x-c)]
+
+@named rossler = ODESystem(eqs)
+
+"""
+rossler equations
+
+```math
+$(latexify(rossler))
+```
+
+[Reference](https://www.sciencedirect.com/science/article/abs/pii/0375960176901018)
+[Wikipedia](https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor)
+
+"""
+prob_ode_rossler = ODEProblem(rossler,[],(0.0,1.0))
+
+
+# rabinovich_fabrikant
+@parameters t a=0.14 b=0.10
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ y*(z-1+x^2) + b*x,
+       D(y) ~ x*(3*z+1-x^2)+b*y,
+       D(z) ~ -2*z*(a+x*y)]
+
+@named rabinovich_fabrikant = ODESystem(eqs)
+
+"""
+rabinovich_fabrikant equations
+
+```math
+$(latexify(rabinovich_fabrikant))
+```
+
+[Reference](https://en.wikipedia.org/wiki/Rabinovich%E2%80%93Fabrikant_equations)
+
+"""
+prob_ode_rabinovich_fabrikant = ODEProblem(rabinovich_fabrikant,[],(0.0,1.0))
+
+
+# sprott
+@parameters t a=2.07 b=1.79
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ y+a*x*y+x*z,
+       D(y) ~ 1-b*x^2+y*z,
+       D(z) ~ x-x^2-y^2]
+
+@named sprott = ODESystem(eqs)
+
+"""
+sprott equations
+
+```math
+$(latexify(sprott))
+```
+
+[Reference](http://sprott.physics.wisc.edu/pubs/paper423.pdf)
+
+"""
+prob_ode_sprott = ODEProblem(sprott,[],(0.0,1.0))
+
+
+# hindmarsh_rose
+@parameters t a=1 b=3 c=1 d=5 r=1e-2 s=4 xr=-8/5 i=5
+@variables x(t)=1 y(t)=0 z(t)=0
+D = Differential(t)
+
+eqs = [D(x) ~ y-a*x^3+b*x^2-z+i,
+       D(y) ~ c-d*x^2-y,
+       D(z) ~ r*(s*(x-xr)-z)]
+
+@named hindmarsh_rose = ODESystem(eqs)
+
+"""
+hindmarsh_rose equations
+
+```math
+$(latexify(hindmarsh_rose))
+```
+
+[Reference](https://en.wikipedia.org/wiki/Hindmarsh%E2%80%93Rose_model)
+
+"""
+prob_ode_hindmarsh_rose = ODEProblem(hindmarsh_rose,[],(0.0,1.0))