This is the phase-space diagram of a system that is itself a modified Thomas system for c=5 and b=0.0.
However, I want to plot a similar figure without solving the equation. It does not need to be as accurate as the phase-space diagram above or the animation of the same below.
This is my code for the graphs:
soln = With[{b = 0.0, c = 5, tmax = 200},
NDSolve[{x'[t] == -b x[t] + Sin[y[t]] + c y[t],
y'[t] == -b y[t] + Sin[z[t]] - c x[t],
z'[t] == -b z[t] + Sin[x[t]], x[0] == 1.0, y[0] == 0.0,
z[0] == 1.0}, {x, y, z}, {t, 0, tmax, 0.1},
MaxSteps -> \[Infinity]]];
Animate[ParametricPlot3D[
Evaluate[{x[t], y[t], z[t]} /. soln], {t, 0, tmax},
PlotPoints -> 500,
Axes -> False,
ColorFunction ->
Function[{x, y, z}, ColorData[{"Rainbow", "Reverse"}][z]],
AspectRatio -> 1, PlotRangePadding -> 1, ImageSize -> 800,
PlotTheme -> "Scientific",
PlotStyle -> Directive[Opacity[0.4]],
PlotRange -> {{-5, 5}, {-5, 5}, {0, 5}}], {tmax, 0.1, 200},
AnimationRate -> 5, AnimationRepetitions -> Infinity]
How can I make a conceptual diagram showing this phase-space portrait with magnetic field lines along the axis of the inner helical trajectories?
How can I plot something like the image below?
NDSolve
)? $\endgroup$NDSolve
. That is the actual phase-space diagram. I don't want to put things into it. So, I needed a model that I can play with to visualize $\endgroup$