Reputation
1,462
Next privilege 2,000 Rep.
Edit questions and answers
Badges
4 15
Newest
 Inquisitive
Impact
~21k people reached

  • 0 posts edited
  • 0 helpful flags
  • 41 votes cast
2d
comment Creating a nonlinear phase portrait
@MichaelE2 For an example, see here and here.
2d
comment Creating a nonlinear phase portrait
@MichaelE2 When you have have a system of two differential equations, x'=f(x,y) and y'=g(x,y), the values of x and y that make f(x,y)=0 is called the nullcline for the first equation, and the values of x and y that make g(x,y)=0 is called the nullcline of the second equations. I have my students draw them in two different colors. Where the orange and green nullclines intersect, you have an equilibrium point. Along the nullcline of the first equation, x'=0, so there is no right and left motion. For the y'=0 nullcline, there is no up and down motion. This helps create phase portraits by hand.
2d
comment Creating a nonlinear phase portrait
@GrishaKirilin Used your suggestion and ran into a small problem. And I am looking for a few more suggestions. See the edits to my post. Thanks for your idea. It is really a good one that I might be able to easily use with my student. I will note however, that StreamStyle -> {Blue, "Line"} doesn't really work. Try StreamStyle -> {Blue, "ArrowArrow"}. Think we've seen these errors before.
2d
revised Creating a nonlinear phase portrait
Updated my work thanks to some nice suggestions by folks and then looked at a second case to see how things went.
Apr
22
comment Plotting separatrices for nonlinear system
@MichaelE2 See what I just did on the following page
Apr
22
comment Creating a nonlinear phase portrait
@MichaelE2 What do you think? Is this a good idea for my students? I am amazed that I found that ExtrapolationHandler thing.
Apr
22
asked Creating a nonlinear phase portrait
Apr
22
comment Strange difficulty with DSolveValue
I just realized I tried that, but the system hung and I had to abort. Now I realize it is because of the nonlinear system and I have to use NDSolveValue. Thanks for the notice.
Apr
22
asked Strange difficulty with DSolveValue
Apr
22
comment A With and ContourPlot difficulty
Thanks everyone. I'm not there yet (got a lot yet to learn), but these responses are helping me along the way.
Apr
22
comment A With and ContourPlot difficulty
@2012rcampion Ah, so it is because I have With[{a=2,b=3,r=1}, followed later by sys, which has no occurrences of a, b, or r, that nothing gets inserted and then things begin?
Apr
22
comment A With and ContourPlot difficulty
@2012rcampion Using Block works, but how come when I look up the With command in the documentation, it says exactly this: "With[{x=x0, y=y0, ...}, expr] specifies that in expr occurrences of the symbols x, y, ... should be replaced with x0, y0, ...." Is it because what I have after the With starting point is not an expression?
Apr
22
asked A With and ContourPlot difficulty
Apr
21
asked Axes in a vector plot
Apr
20
comment Plotting separatrices for nonlinear system
@MichaelE2 Excellent answer, easily understood by me. May I now ask my next question? This command is puzzling: sepPlots = ParametricPlot @@@ ({{x[t], y[t]}, Hold[Flatten][{t, x["Domain"]}]} /. separatrices // ReleaseHold); Could you add a nice explanation of this above?
Apr
20
comment Plotting separatrices for nonlinear system
You were both equally helpful. I really appreciate your answers. I'm going to have to give a little effort to understand the coding.
Apr
20
comment Plotting separatrices for nonlinear system
@MichaelE2 Absolutely wonderful answer. But I am having difficulty figuring it out. My best first question is what does (sys /. v : x | y :> v[t]) mean? I know that sys is {x (1 - x - y), (4 - 7 x - 3 y) y}. Then (sys /. v : x | y :> v[t]) returns {x[t] (1 - x[t] - y[t]), (4 - 7 x[t] - 3 y[t]) y[t]}. So it seems to replace x with x[t] and y with y[t], but why? What does v:x | y:>v[t] mean?
Apr
20
accepted Plotting separatrices for nonlinear system
Apr
19
revised Plotting separatrices for nonlinear system
added 2914 characters in body
Apr
19
comment Plotting separatrices for nonlinear system
Beautiful! I definitely can use this in class. However, what I need is the same image, but with the separatrices, the solutions moving toward and away from the equilibrium point.