From cb03cd375be045db4bcfca54040c85bff4ed54be Mon Sep 17 00:00:00 2001 From: Datseris Date: Tue, 22 Mar 2022 10:03:34 +0100 Subject: [PATCH] Commit 22-Mar-22, printed first edition --- .gitignore | 3 + Manifest.toml | 1496 +++++++++-------- Project.toml | 5 +- README.md | 9 +- animations/4/logistic_cobweb.jl | 8 - animations/4/logistic_intermittency.jl | 15 + ...bitdiagram.jl => logistic_orbitdiagram.jl} | 0 cover.png | Bin 0 -> 786951 bytes figure_generation/1/1.1.jl | 4 +- figure_generation/10/10.2.jl | 2 +- figure_generation/10/10.5.jl | 13 +- figure_generation/10/10.8.jl | 2 +- figure_generation/10/10.9.jl | 2 +- figure_generation/11/11.7.jl | 2 +- .../11/11.7_calculate_kse_lyapunovs.jl | 1 - figure_generation/2/2.4.jl | 8 +- figure_generation/5/5.6.jl | 3 +- figure_generation/7/7.5.jl | 18 +- sample/sample.pdf | Bin 6753450 -> 4434992 bytes 19 files changed, 875 insertions(+), 716 deletions(-) create mode 100644 animations/4/logistic_intermittency.jl rename animations/4/{orbitdiagram.jl => logistic_orbitdiagram.jl} (100%) create mode 100644 cover.png diff --git a/.gitignore b/.gitignore index 0383551..f3fa732 100644 --- a/.gitignore +++ b/.gitignore @@ -12,6 +12,9 @@ testing corrections_for_proof *.pptx *.docx +second_edition +printed_versions +proof ################################################################################ # DrWatson Project Structure # diff --git a/Manifest.toml b/Manifest.toml index 3cace42..0b2a46f 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -1,1892 +1,2030 @@ # This file is machine-generated - editing it directly is not advised -[[AbstractFFTs]] -deps = ["LinearAlgebra"] -git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0" +julia_version = "1.7.0" +manifest_format = "2.0" + +[[deps.AbstractFFTs]] +deps = ["ChainRulesCore", "LinearAlgebra"] +git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4" uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" -version = "1.0.1" +version = "1.1.0" 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+[[deps.x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" diff --git a/Project.toml b/Project.toml index 798da88..0849466 100644 --- a/Project.toml +++ b/Project.toml @@ -22,12 +22,12 @@ FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" GraphMakie = "1ecd5474-83a3-4783-bb4f-06765db800d2" +Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6" ImageMagick = "6218d12a-5da1-5696-b52f-db25d2ecc6d1" InteractiveDynamics = "ec714cd0-5f51-11eb-0b6e-452e7367ff84" Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" JLD = "4138dd39-2aa7-5051-a626-17a0bb65d9c8" JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" -LightGraphs = "093fc24a-ae57-5d10-9952-331d41423f4d" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" @@ -48,9 +48,10 @@ TimeseriesSurrogates = "c804724b-8c18-5caa-8579-6025a0767c70" TransferEntropy = "ea221983-52f3-5440-99c7-13ea201cd633" [compat] +Agents = "5" ChaosTools = "2" DelayEmbeddings = "2" -DynamicalSystemsBase = "2" +DynamicalSystemsBase = "2.3.10" Entropies = "1" RecurrenceAnalysis = "1.6" julia = "1.5" diff --git a/README.md b/README.md index 7ce7b14..be50ddd 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,11 @@ # Nonlinear Dynamics: A concise introduction interlaced with code -This repository holds the material related with the textbook _Nonlinear Dynamics: A concise introduction interlaced with code_, co-authored by George Datseris and Ulrich Parlitz. This textbook will be published by Springer, in the series Undergraduate Lecture Notes in Physics, in 2021. +![**Nonlinear Dynamics: A concise introduction interlaced with code**](cover.png) + +This repository holds material related with the textbook _Nonlinear Dynamics: A concise introduction interlaced with code_, co-authored by George Datseris and Ulrich Parlitz. The textbook will be published by Springer-Nature, in the series Undergraduate Lecture Notes in Physics. + +> https://link.springer.com/book/10.1007/978-3-030-91032-7 + **Please do not open issues to ask questions on installing and running Julia or Julia packages, or questions on nonlinear dynamics in this repository.** Instead, open issues directly related with the book: found typos, problems with the source code contained here, suggestions for improvement of existing book sections, suggestions for new book sections, contributing new exercises, new multiple choice questions, etc. All contributions will be properly acknowledged whenever a new edition is out. @@ -13,7 +18,7 @@ This repository holds the material related with the textbook _Nonlinear Dynamics 6. [Interactive applications and videos](#interactive-applications-and-videos) ## Sample material -Sample material *(currently preliminary)* of the book is contained as `.pdf` in the `sample` folder. +A sample of 10% the book length is contained as `.pdf` in the `sample` folder. ## Tutorials for Julia and related packages Below we provide links to various sources for learning Julia, or the packages that we use in the code snippets in the book. diff --git a/animations/4/logistic_cobweb.jl b/animations/4/logistic_cobweb.jl index 46ae607..4474f9b 100644 --- a/animations/4/logistic_cobweb.jl +++ b/animations/4/logistic_cobweb.jl @@ -10,11 +10,3 @@ fkwargs = [(linewidth = 4.0, color = COLORSCHEME[i+1]) for i in 1:3] rrange = 1:0.001:4.0 fig = interactive_cobweb(lo, rrange, 2; fkwargs) record_interaction(fig, projectdir("animations", "4", "logistic_cobweb.mp4")) - -# %% the second range is a convenience for intermittency example of logistic -rrange = (rc = 1 + sqrt(8); [rc - 1e-3, rc - 1e-5, rc]) -fig = interactive_cobweb(lo, rrange, 3; fkwargs) -record_interaction( - fig, projectdir("animations", "4", "logistic_intermittency.mp4"); - total_time=15, sleep_time = 2 -) diff --git a/animations/4/logistic_intermittency.jl b/animations/4/logistic_intermittency.jl new file mode 100644 index 0000000..47b7981 --- /dev/null +++ b/animations/4/logistic_intermittency.jl @@ -0,0 +1,15 @@ +# Logistic map cobweb and timeseries +using DrWatson +@quickactivate "NonlinearDynamicsTextbook" +include(srcdir("colorscheme.jl")) +using GLMakie, DynamicalSystems, InteractiveDynamics + +lo = Systems.logistic(0.4; r=rrange[1]) +fkwargs = [(linewidth = 4.0, color = COLORSCHEME[i+1]) for i in 1:3] + +rrange = (rc = 1 + sqrt(8); [rc - 1e-3, rc - 1e-5, rc]) +fig = interactive_cobweb(lo, rrange, 3; fkwargs) +record_interaction( + fig, projectdir("animations", "4", "logistic_intermittency.mp4"); + total_time=15, sleep_time = 2 +) diff --git a/animations/4/orbitdiagram.jl 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zBP=XLqhJMguyS?fR5P;xn7LTe$T$I=%^W>%bUX#&I%xl^!_o?5;bQ0PYUkvL0Md9b zO`|9$BfujpAi&A{hDWD-{ykin>A%82Gep%Ylh(F2y(Wvu(P(avaIp*`v{kK`9BFOM@u_1M+66uxmE*- z47`Z&e?`u=POeVy<328S76@?VH8hGV@N&}smAg2BL7dK3E}S5^h%*8YFaO(I{z+`O O47}GLWg*h0LH`F}6w(0z literal 0 HcmV?d00001 diff --git a/figure_generation/1/1.1.jl b/figure_generation/1/1.1.jl index 3801288..54bdf43 100644 --- a/figure_generation/1/1.1.jl +++ b/figure_generation/1/1.1.jl @@ -53,9 +53,9 @@ llw = 2.0 tr = trajectory(ds, 100; Ttr = 100, Δt = 0.01) axlo3d.plot3D(columns(tr)..., color = cs[1], lw = llw/2) tr = trajectory(ds, 10; Ttr = 1000, Δt = 0.01) -axlo3d.plot3D(columns(tr)..., color = cs[2], lw = llw) +axlo3d.plot3D(columns(tr)..., color = cs[3], lw = 2llw) tr = trajectory(ds, 10, [10,20,40.0]; Ttr = 10, Δt = 0.01) -axlo3d.plot3D(columns(tr)..., color = cs[3], lw = llw) +axlo3d.plot3D(columns(tr)..., color = cs[2], lw = llw) axlo3d.set_xlabel("\$x\$", labelpad = -10) axlo3d.set_ylabel("\$y\$", labelpad = -10) axlo3d.set_zlabel("\$z\$", labelpad = -10) diff --git a/figure_generation/10/10.2.jl b/figure_generation/10/10.2.jl index 30794f8..64fcbc7 100644 --- a/figure_generation/10/10.2.jl +++ b/figure_generation/10/10.2.jl @@ -2,7 +2,7 @@ using DrWatson @quickactivate "NonlinearDynamicsTextbook" include(srcdir("colorscheme.jl")) import GLMakie, GraphMakie -using GraphMakie.NetworkLayout, LightGraphs +using GraphMakie.NetworkLayout, Graphs n0 = 25 seed = 42 diff --git a/figure_generation/10/10.5.jl b/figure_generation/10/10.5.jl index 7a4bd23..3c3a6de 100644 --- a/figure_generation/10/10.5.jl +++ b/figure_generation/10/10.5.jl @@ -4,7 +4,7 @@ using DrWatson @quickactivate "NonlinearDynamicsTextbook" include(srcdir("style.jl")) -using DynamicalSystems, PyPlot +using DynamicalSystems, PyPlot, Random, OrdinaryDiffEq function chimera_ODE(du,u,p,t) ω, R, alpha, nosc = p @@ -81,11 +81,12 @@ for its = 1:nts end end -im1 = axs[1+axi].pcolormesh(tvec,indx,qmat,cmap = "inferno") -axs[1+axi].set_xlabel(L"t"; labelpad = -20) -axs[axi+1].set_ylabel(L"i"; labelpad = -20) -axs[axi+1].set_yticks([indx[1], indx[end]]) -axs[axi+1].set_xticks([0, tvec[end]]) +im1 = axs[1+axi].pcolormesh(indx,tvec,qmat',cmap = "inferno") +axs[1+axi].set_ylabel(L"t"; labelpad = -20) +axs[axi+1].set_yticks([0, tvec[end]]) +axs[axi+1].set_yticklabels(["0", "T"]) +axs[axi+1].set_xlabel(L"i"; labelpad = -20) +axs[axi+1].set_xticks([indx[1], indx[end]]) if axi == 2 diff --git a/figure_generation/10/10.8.jl b/figure_generation/10/10.8.jl index b8271d4..fa95585 100644 --- a/figure_generation/10/10.8.jl +++ b/figure_generation/10/10.8.jl @@ -46,7 +46,7 @@ xlabel(L"$t$") ax = gca() ax.set_xlim([0.,120.]) # ax.set_ylim([-2.1,2.5]) -ax.legend([L"S/N"; L"I/N"; L"R/N"], fontsize = 25) +ax.legend([L"S/N"; L"R/N"; L"I/N";], fontsize = 25) fig.tight_layout(pad=0.3) # save diff --git a/figure_generation/10/10.9.jl b/figure_generation/10/10.9.jl index 4765559..5e89e87 100644 --- a/figure_generation/10/10.9.jl +++ b/figure_generation/10/10.9.jl @@ -1,7 +1,7 @@ using DrWatson @quickactivate "NonlinearDynamicsTextbook" include(srcdir("style.jl")) -using Agents, LightGraphs, DataFrames +using Agents, Graphs, DataFrames # import GLMakie # using GraphMakie.NetworkLayout diff --git a/figure_generation/11/11.7.jl b/figure_generation/11/11.7.jl index a13bbed..080ef0c 100644 --- a/figure_generation/11/11.7.jl +++ b/figure_generation/11/11.7.jl @@ -15,7 +15,7 @@ saveat = 0:dt:T dt = 0.25 dx = 0.2 # spatial discretization xs = range(0, b1, step = dx) # space -u0 = @. cos(xs) + 0.1*sin(xs/8) + 0.01*cos((2π/b)*xs) +u0 = @. cos(xs) + 0.1*sin(xs/8) + 0.01*cos((2π/b1)*xs) ks = Vector(FFTW.rfftfreq(length(u0))/dx) # conjugate space (wavenumbers) forward_plan = FFTW.plan_rfft(u0) diff --git a/figure_generation/11/11.7_calculate_kse_lyapunovs.jl b/figure_generation/11/11.7_calculate_kse_lyapunovs.jl index a51e783..6977ad8 100644 --- a/figure_generation/11/11.7_calculate_kse_lyapunovs.jl +++ b/figure_generation/11/11.7_calculate_kse_lyapunovs.jl @@ -128,7 +128,6 @@ b = 20 # length of spatial domain N = 4000 # steps to run the QR normalization Δt = 1.0 # timestep between normalizations dx = 0.2 # spatial discretization -kport = 0.5 for b in 20:20:60 if b == 20 diff --git a/figure_generation/2/2.4.jl b/figure_generation/2/2.4.jl index 0c76310..1a77231 100644 --- a/figure_generation/2/2.4.jl +++ b/figure_generation/2/2.4.jl @@ -18,12 +18,13 @@ xgrid = -0.3:0.02:1.1 ygrid = -0.1:0.01:0.4 function add_nullclines!(ax, a, b, ε, I) - u = -0.3:0.01:1.1 + u = -0.5:0.01:1.1 w1 = @. u w2 = @. a*u*(u-b)*(1-u) + I ax.plot(u, w1, "--", color = "C3", lw = 2.0) ax.plot(u, w2, ":", color = "C5") - ax.set_ylim(ygrid[1], ygrid[end]) # why is this necessary? + ax.set_xlim(xgrid[1], xgrid[end]) # plotting nullclines changes limits + ax.set_ylim(ygrid[1], ygrid[end]) end function add_streamlines!(ax, a, b, ε, I) @@ -86,6 +87,7 @@ ax.set_ylabel("\$w\$"; labelpad = -20) ax.set_xlabel("\$u\$"; labelpad = -20) ax.set_xticks([0, 1]) ax.set_yticks([0, 0.4]) +ax.set_xlim(-0.3, 1.15) zbox = ((-0.05, -0.04), (0.25, 0.04)) axis_zoomin!(axs[5],axs[3], zbox, zbox, "C2"; lw = 1.0) @@ -149,6 +151,7 @@ ax.set_ylabel("\$w\$"; labelpad = -20) ax.set_xlabel("\$u\$"; labelpad = -20) ax.set_xticks([0, 1]) ax.set_yticks([0, 1]) +ax.set_xlim(-0.3, 1.15) # Fig F: limit cycle # ------------------------- @@ -169,6 +172,7 @@ ax.set_ylabel("\$w\$"; labelpad = -20) ax.set_xlabel("\$u\$"; labelpad = -20) ax.set_xticks([0, 1]) ax.set_yticks([0, 0.6]) +ax.set_xlim(-0.5, 1.1) add_identifiers!(fig) fig.subplots_adjust(bottom = 0.08, left = 0.05, top = 0.95, right = 0.97, hspace = 0.2) diff --git a/figure_generation/5/5.6.jl b/figure_generation/5/5.6.jl index f638c3c..31ce2b0 100644 --- a/figure_generation/5/5.6.jl +++ b/figure_generation/5/5.6.jl @@ -26,7 +26,8 @@ for (j, (ax, x)) in enumerate(zip(axs, (-5:0, -10:0))) ax.axvspan(x[1], x[end], color = COLORS[4], alpha = 0.25) ax.grid("on") ax.plot(x, Dl, c = COLORS[3]) - ax.text(x[2] + 1.5 + 0.5*(j-1), Dl[2], "\$D_2\$ = $D", color = COLORS[3], size = 30) + dimlabel = j == 1 ? "\$\\Delta_2^{(H)}\$" : "\$\\Delta^{(C)}\$" + ax.text(x[2] + 1.5 + 0.5*(j-1), Dl[2], "$(dimlabel) ≈ $D", color = COLORS[3], size = 30) end xtick = -11:3:1 diff --git a/figure_generation/7/7.5.jl b/figure_generation/7/7.5.jl index f7fb380..a04a004 100644 --- a/figure_generation/7/7.5.jl +++ b/figure_generation/7/7.5.jl @@ -15,7 +15,8 @@ x .+= randn(length(x))*std(x)*0.1 # generate autoregressive process Random.seed!(77163) -η = randn(5000) +rng = Random.MersenneTwister(77163) +η = randn(rng, 5000) s = ones(5000) for n in 4:5000 s[n] = 1.625s[n-1] - 0.284s[n-2] - 0.355s[n-3] + η[n] - 0.96η[n-1] @@ -23,15 +24,14 @@ end s ./= std(s) # Do the surrogate calculation -εro, εma = std.((x, s))./4 algs = [RandomFourier(), AAFT()] names = ["FT", "AAFT"] sgx = [surrogenerator(x, m) for m in algs] -sgs = [surrogenerator(s, m) for m in algs] +sgs = [surrogenerator(s, m, rng) for m in algs] τx = estimate_delay(x, "ac_zero") τs = estimate_delay(s, "ac_zero") -Cx = grassberger(embed(x, 3, τx)) -Cs = grassberger(embed(s, 4, τs)) +Cx = takens_best_estimate(embed(x, 3, τx), 0.25)[1] +Cs = takens_best_estimate(embed(s, 4, τs), 0.25)[1] A = length(algs) xboxes = [] @@ -42,8 +42,8 @@ for i in 1:A for j in 1:100 X = embed(sx(), 3, τx) S = embed(ss(), 4, τs) - push!(bx, grassberger(X)) - push!(bs, grassberger(S)) + push!(bx, takens_best_estimate(X, 0.25)[1]) + push!(bs, takens_best_estimate(S, 0.25)[1]) end push!(xboxes, bx) push!(sboxes, bs) @@ -83,8 +83,8 @@ axs[2].plot(l, fill(Cx, 2), color = "C0", ls = "dashed") axs[3].plot(l, fill(Cs, 2), color = "C2", ls = "dashed") # axs[2].set_ylim(2.7, 3) axs[2].set_yticks(2.6:0.2:3.0) -axs[2].set_title("\$\\Delta^{(C)}\$, Rössler") -axs[3].set_title("\$\\Delta^{(C)}\$, ARMA") +axs[2].set_title("\$\\Delta^{(T)}\$, Rössler") +axs[3].set_title("\$\\Delta^{(T)}\$, ARMA") axs[3].set_yticks(3.4:0.3:4.1) for ax in axs[2:3] diff --git a/sample/sample.pdf b/sample/sample.pdf index 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