Phase portraits of differential equations

Hi all,

I am trying to sketch the phase portraits of the following differential equations, seperately

x˙ = 1 − 2 cos x

and

x˙=-x + 1/(1 + e^(-8 x)) - 0.5

I used some existing matlab codes that i found however it wasnt possible to draw the phase portraits.

Could you please help me with this?

Thank you very much

Answer 1

[Sulaymon Eshkabilov]

Step 1. Take a derivative of your function 1 (F1) and 2 (F2) and save them dF1 and dF2. You can use syms x and diff() here.

Step 2. Compute their values (F1(x), F2(x), dF1(x), dF2(x)) at x (e.g.: x = -pi... pi). You can use subs() or just plugin the values of x into the expressions of F1, F2, dF1, dF2.

Step 3. Plot the computed values: F1 vs. dF1 in Figure 1 and F2 vs. dF2 in Figure 2. This is a phase plot.