Fig 1.7

For Figures 1.7, 7.13, 7.14, 7.15.

using OrdinaryDiffEq
using DiffEqCallbacks
using ComponentArrays
using Plots
Plots.default(linewidth=2)

Convenience functions

hil(x, k) = x / (x + k)
hil(x, k, n) = hil(x^n, k^n)
hil (generic function with 2 methods)

Collins toggle switch model

function collins!(du, u, p, t)
    a1, a2, β, γ, i1, i2 = p
    s1, s2 = u
    du[1] = a1 * hil(1 + i2, s2, β) - s1
    du[2] = a2 * hil(1 + i1, s1, γ) - s2
    nothing
end
collins! (generic function with 1 method)

Setup the problem

tspan = (0.0, 50.0)
ps = [3.0, 2.5, 4.0, 4.0, 0.0, 0.0] # a1, a2, β, γ, i1, i2
u0 = [0.075, 2.5] # s1, s2
prob = ODEProblem(collins!, u0, tspan, ps)
ODEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 50.0)
u0: 2-element Vector{Float64}:
 0.075
 2.5

Callbacks

affect_i2_on!(integrator) = integrator.p[6] = 10.0
affect_i2_off!(integrator) = integrator.p[6] = 0.0
affect_i1_on!(integrator) = integrator.p[5] = 10.0
affect_i1_off!(integrator) = integrator.p[5] = 0.0
cb_i2_on = PresetTimeCallback(10.0, affect_i2_on!)
cb_i2_off = PresetTimeCallback(20.0, affect_i2_off!)
cb_i1_on = PresetTimeCallback(30.0, affect_i1_on!)
cb_i1_off = PresetTimeCallback(40.0, affect_i1_off!)
cbs = CallbackSet(cb_i2_on, cb_i2_off, cb_i1_on, cb_i1_off)
SciMLBase.CallbackSet{Tuple{}, Tuple{SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}, typeof(Main.var"##283".affect_i2_on!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}, SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}, typeof(Main.var"##283".affect_i2_off!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}, SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}, typeof(Main.var"##283".affect_i1_on!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}, SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}, typeof(Main.var"##283".affect_i1_off!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}}}((), (SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}, typeof(Main.var"##283".affect_i2_on!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}(DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}([10.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i2_on!), Main.var"##283".affect_i2_on!, DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_on!)}([10.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i2_on!), SciMLBase.FINALIZE_DEFAULT, Bool[1, 1], nothing, ()), SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}, typeof(Main.var"##283".affect_i2_off!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}(DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}([20.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i2_off!), Main.var"##283".affect_i2_off!, DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i2_off!)}([20.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i2_off!), SciMLBase.FINALIZE_DEFAULT, Bool[1, 1], nothing, ()), SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}, typeof(Main.var"##283".affect_i1_on!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}(DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}([30.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i1_on!), Main.var"##283".affect_i1_on!, DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_on!)}([30.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i1_on!), SciMLBase.FINALIZE_DEFAULT, Bool[1, 1], nothing, ()), SciMLBase.DiscreteCallback{DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}, typeof(Main.var"##283".affect_i1_off!), DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}, typeof(SciMLBase.FINALIZE_DEFAULT), Nothing, Tuple{}}(DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}([40.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i1_off!), Main.var"##283".affect_i1_off!, DiffEqCallbacks.PresetTimeFunction{Vector{Float64}, typeof(SciMLBase.INITIALIZE_DEFAULT), typeof(Main.var"##283".affect_i1_off!)}([40.0], true, SciMLBase.INITIALIZE_DEFAULT, Main.var"##283".affect_i1_off!), SciMLBase.FINALIZE_DEFAULT, Bool[1, 1], nothing, ())))

Solve the problem

@time sol = solve(prob, callback=cbs)
  6.155512 seconds (17.89 M allocations: 919.428 MiB, 2.26% gc time, 99.98% compilation time)
retcode: Success
Interpolation: 3rd order Hermite
t: 45-element Vector{Float64}:
  0.0
  0.38548049109061366
  1.2786313586853497
  2.464538731594535
  4.06089298356771
  6.199065127274195
  9.163107137014421
 10.0
 10.0
 10.90492160678711
  ⋮
 37.811045850454185
 38.97117380017039
 40.0
 40.0
 41.45655048835799
 43.01214443871626
 45.107570048628844
 47.65220584313297
 50.0
u: 45-element Vector{Vector{Float64}}:
 [0.075, 2.5]
 [0.07496310584167308, 2.4999747263084022]
 [0.0749189538414308, 2.499943104158718]
 [0.0748994736010588, 2.49992797574084]
 [0.07489347508722315, 2.4999227222886917]
 [0.07489238103870041, 2.4999215657222047]
 [0.07489230549277733, 2.4999214349680683]
 [0.07489223296465886, 2.49992138933308]
 [0.07489223296465886, 2.49992138933308]
 [1.8138876963707786, 1.6074955381407825]
 ⋮
 [0.07794218751213773, 2.498990428766632]
 [0.07588614749855138, 2.499682949330218]
 [0.0752553715213293, 2.4998865900140177]
 [0.0752553715213293, 2.4998865900140177]
 [0.07497917389522026, 2.4999126610145854]
 [0.07491123383177441, 2.499919371700559]
 [0.07489514451004411, 2.4999210438808794]
 [0.07489273938700679, 2.499921301318458]
 [0.07489227301035209, 2.4999213465656758]

Visual

plot(sol, legend=:right, xlabel = "Time", ylabel="Concentration", title="Fig 1.7", labels=["s1" "s2"])

This notebook was generated using Literate.jl.

Back to top