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I wrote below the instructions in Mathematica because I wanted to see the phase portrait of systems of DE of $4\times 4$ dimension. But Mathematica cannot recognize the last 2 variables $y$ and $z$ and marks an error.

What can I do to solve this problem?

StreamPlot[{b n - d w - w β x - w β1 y,
            β w x - x (d - c - γ),
            β1 w y - (d + c1 + γ1) y,
            γ x + γ1 y - d z},
  {w, -5, 5}, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}]
Improve this question
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    $\begingroup$ Maybe I misunderstand what you're trying to do, but it looks like you're trying to make a 4D plot, which is pretty clearly impossible. I think you need to look at the syntax of StreamPlot in the documentation. $\endgroup$
    – b3m2a1
    Commented Jan 23, 2018 at 4:12
  • $\begingroup$ @b3m2a1 It's not actually a 4D plot it's a 4D phase portrait. $\endgroup$
    – user441848
    Commented Jan 23, 2018 at 4:16
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    $\begingroup$ So... what do you expect it to look like? What is the expected output, if not a 4D plot? From what I remember of my DEs, phase portraits are in general 2D objects, thus there are 2 independent variables and maybe a parametrized curve laid on top. What do you want the x, y, and z variables to do? $\endgroup$
    – b3m2a1
    Commented Jan 23, 2018 at 4:20
  • $\begingroup$ @b3m2a1, @ OP: For an autonomous system, a "phase portrait" is a plot of some flow lines in phase space. The dimension of phase space is equal to the number of independent variables, which as you correctly say is four. 2D phase portraits are relatively easy to plot and read. Mathematica can plot 3D phase portraits, but they are not particularly easy to read. There is no built-in support for 4D visualization, so folks have to do their own projections down to 3D and render the result, which is even harder to read. $\endgroup$
    – Michael E2
    Commented Jan 23, 2018 at 12:49
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    $\begingroup$ The paper, doi.org/10.1016/j.physleta.2005.12.030, tries to visualize a 4D system by projecting onto the 6 coordinate planes corresponding to all 6 pairs of the four variables. This would be possible. Once you select the flow lines, it would be easy. Don't know if it would be particularly useful though. $\endgroup$
    – Michael E2
    Commented Jan 23, 2018 at 12:52

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