Can someone please explain to me how to draw the PP, I mean besides drawing the lines which i think i can understand, how do you decide how to draw the direction of the phase portrait?(adsbygoogle = window.adsbygoogle || []).push({});

I mean for example we have: x'=y and y'=-2x^3, obviously those are parabolas and hyperbolas, now the equilibrium point is (x,y)=(0,0)

for x=1 y=-1 y'=-2 so the direction should be decided by the fact that y'/x'=dy/dx=tg(a)>0 so it's going counter clockwise for the hyperbola in the fourth quardant, for x=1 y=1 it's negative then it goes clockwise, the same is for x=-1 y=1 it's counterclockwise, and for x=-1 y=-1 it's clockwise, have i got it correct, it's all about identifiy the clockwise anti clockwise by dy/dx, correct?

Well, I think I got it, unless someone thinks otherwise, do tell me if i got it correct?

thanks.

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# Drawing phase portraits.

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