Using Parallelize to Visualize StreamPlot

Questions
,
1

I am trying to figure out if multiple parameter system ODEs, can be modeled using Parallelize and StreamPlot.

For example, we have:

  Parallelize[
   Map[StreamPlot[#, {x, -3, 3}, {y, -3, 3}] &, 
    Flatten[Table[ {x^i y^j, x^j y^i}, {i, 2}, {j, 2}], 1]]]

Is there a slick way to use this command to better visualize stream plots for a system like

dx/dt = (a-by)x \\ dy/dt = (cx-d)y

It has four parameters, so I was wondering if we can use parallelize to fix a parameter at a time and visually see a bunch of stream plots?

2

Parallelize changes how the calculations are done internally. It doesn’t change how the results are represented. Parallelize won’t do anything to change or improve a visualization.

Are you looking to layer multiple plots on top of each other? This can be done with “Show”:

reference.wolfram.com/language/ref/Show.html

If you do want to layer multiple plots together, I would first making them separate colors so that the different layers can be distinguished.