Commit 25-Oct-21, submitted version

add animations folder

animations/11/Brusselator.jl

@@ -0,0 +1,38 @@
+# This file needs `src/brusselator_produce.jl` to have run with appropriate parameters.
+# The `saveat` parameter of that file is the time output of the frames.
+using DrWatson
+@quickactivate "NonlinearDynamicsTextbook"
+include(srcdir("colorscheme.jl"))
+using Random, OrdinaryDiffEq
+import GLMakie
+
+a = 9.0
+b = 10.2
+L = 50.0 # size of domain
+N = 250  # no. of grid points
+d = 1.7
+
+prefix = "brusselator2D_dense"
+fname = savename(prefix, @strdict(a, b, d, L, N, ic), "jld2")
+data = load(datadir("Brusselator", fname))
+uout = data["u"]
+tvec = data["t"]
+
+heatobs = GLMakie.Observable(uout[1][1,:,:])
+tobs = GLMakie.Observable(0.0)
+titobs = GLMakie.lift(t -> "t = $(t)", tobs)
+
+fig = GLMakie.Figure(resolution = (600, 550))
+ax = fig[1,1] = GLMakie.Axis(fig; title = titobs)
+hmap = GLMakie.heatmap!(ax, heatobs; colormap = :inferno, colorrange = (0, 1.5))
+cb = GLMakie.Colorbar(fig[1, 2], hmap; width = 20)
+display(fig)
+
+GLMakie.record(
+        fig, projectdir("animations", "11", "brusselator_d=$(d)_b=$(b).mp4"), 
+        1:length(tvec); framerate = 15
+    ) do i
+
+    tobs[] = tvec[i]
+    heatobs[] = uout[i][1,:,:]
+end

animations/11/fitzhigh_various.jl

@@ -0,0 +1,139 @@
+using DrWatson
+@quickactivate "NonlinearDynamicsTextbook"
+include(srcdir("colorscheme.jl"))
+using Random, OrdinaryDiffEq
+import GLMakie
+
+function FitzHugh_Nagumo_ODE(du,u,p,t)
+    a, b, d, epsilon, hsq6 = p
+    uu = @view u[1,:,:]
+    vv = @view u[2,:,:]
+
+    # This code can be optimized a lot if time allows
+    # Create padded u matrix to incorporate Newman boundary conditions - 9-point stencil
+    uuu=[ [uu[2,2] uu[2,:]' uu[2,end-1] ] ; [ uu[:,2] uu uu[:,end-1] ] ; [ uu[end-1,2] uu[end-1,:]' uu[end-1,end-1] ] ]
+    diff_term = d .* ( 
+        4 .* (uuu[2:end-1,1:end-2] .+ uuu[2:end-1,3:end] .+ 
+            uuu[3:end,2:end-1] .+ uuu[1:end-2,2:end-1] ) .+ 
+            uuu[3:end,3:end] .+ uuu[3:end,1:end-2] .+ uuu[1:end-2,3:end] .+ 
+            uuu[1:end-2,1:end-2] .- 20 .*uu  
+    ) ./ hsq6  
+
+    du[1,:,:] = a .* uu .*(1 .-uu).*(uu.-b) .- vv .+ diff_term
+    du[2,:,:] = epsilon .* (uu .- vv )
+end
+
+# --------------------------  main program  -----------------------------
+
+@time begin
+
+# parameters
+L = 300   # size of domain
+N = 150   # no. of grid points
+h = L/N # spatial steps size
+hsq6 = 6*h*h
+
+# FHN parameters
+a = 3.    
+b = 0.2   
+d = 1.   #  diffusion
+epsilon = 0.01 
+
+# open figure
+kplt = 0  # no. of subplot
+
+allsols = []
+allts = []
+
+for ic = 1:2    # initial conditions ( = rows of the plot )
+
+println("ic=",ic)
+
+uu = zeros(N,N)
+vv = zeros(N,N)   
+Random.seed!(13371)
+uu = uu .+ 0.01*randn(N,N)    # random perturbation
+
+# local stimulius = concentric waves
+if ic == 1 
+   uu[40:41,40:41] .= 0.999
+   uu[75:76,75:76] .= 0.999
+end
+
+# local stimulius = spiral waves
+if ic == 2
+   uu[1:end,10:11] .= 0.999
+end   
+
+# initial values   
+u0 = zeros(2,N,N)
+u0[1,:,:] = uu
+u0[2,:,:] = vv 
+
+p = a, b, d, epsilon, hsq6 
+
+if ic == 1
+    saveat = 0.0:2:600
+    tspan = (saveat[1], saveat[end])
+
+    prob = ODEProblem(FitzHugh_Nagumo_ODE, u0, tspan, p)
+    sol = solve(prob, Tsit5(); reltol=1e-6, abstol=1e-6, maxiters = 1e7, saveat)
+    tvec = sol.t
+    uout = [u[1, :, :] for u in sol.u]
+    push!(allsols, uout)
+    push!(allts, tvec)
+
+elseif ic == 2
+    saveat = 0.0:2.0:300.0
+    tspan = (saveat[1], saveat[end])
+    prob = ODEProblem(FitzHugh_Nagumo_ODE, u0, tspan, p)
+    sol = solve(prob, Tsit5(); reltol=1e-6, abstol=1e-6, maxiters = 1e7, saveat)
+
+    uout = [u[1, :, :] for u in sol.u]
+    # second perturbation line
+    u = sol.u[end]
+    u[1, 55:73,1:70] .= 0.999
+    saveat = 300.0:2:900
+    tspan = (saveat[1], saveat[end])
+    prob = ODEProblem(FitzHugh_Nagumo_ODE, u, tspan, p)
+    sol = solve(prob, Tsit5(); reltol=1e-6, abstol=1e-6, maxiters = 1e7, saveat)
+
+    tvec = sol.t
+    uout2 = [u[1, :, :] for u in sol.u]
+    append!(uout, uout2)
+    push!(allsols, uout)
+    push!(allts, tvec)
+
+end
+end # ic loop
+end # cputime
+
+
+# %% Animate
+names = ("concentric", "plane_to_spiral")
+
+for i in (1,2)
+    name = names[i]
+    uout = allsols[i]
+    tvec = allts[i]
+
+    heatobs = GLMakie.Observable(uout[1])
+    tobs = GLMakie.Observable(0.0)
+    titobs = GLMakie.lift(t -> "t = $(t)", tobs)
+
+    fig = GLMakie.Figure(resolution = (600, 550))
+    ax = fig[1,1] = GLMakie.Axis(fig; title = titobs)
+    hmap = GLMakie.heatmap!(ax, heatobs; colormap = :tokyo, colorrange = (-0.2, 1))
+    cb = GLMakie.Colorbar(fig[1, 2], hmap; width = 20)
+    display(fig)
+
+    GLMakie.record(
+        fig, projectdir("animations", "11", "fitzhugh_$(name).mp4"), 
+        1:length(tvec); framerate = 15
+    ) do i
+
+        tobs[] = tvec[i]
+        heatobs[] = uout[i]
+    end
+
+end

animations/11/fitzhugh_spiral.jl

@@ -0,0 +1,28 @@
+# uses file produced by `11.6_produce.jl`.
+using DrWatson
+@quickactivate "NonlinearDynamicsTextbook"
+include(srcdir("colorscheme.jl"))
+using Random, OrdinaryDiffEq
+import GLMakie
+
+data = wload(datadir("FitzHugh", "spiralwave.jld2"))
+@unpack uout, tvec, params = data
+
+heatobs = GLMakie.Observable(uout[1][1,:,:])
+tobs = GLMakie.Observable(0.0)
+titobs = GLMakie.lift(t -> "t = $(t)", tobs)
+
+fig = GLMakie.Figure(resolution = (600, 550))
+ax = fig[1,1] = GLMakie.Axis(fig; title = titobs)
+hmap = GLMakie.heatmap!(ax, heatobs; colormap = :tokyo, colorrange = (-0.2, 1))
+cb = GLMakie.Colorbar(fig[1, 2], hmap; width = 20)
+display(fig)
+
+GLMakie.record(
+        fig, projectdir("animations", "11", "fitzhugh_spiralwave.mp4"), 
+        1:length(tvec); framerate = 15
+    ) do i
+
+    tobs[] = tvec[i]
+    heatobs[] = uout[i][1,:,:]
+end