Phase portraits of differential equations
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Ilias Minas on 31 Oct 2021
I am trying to sketch the phase portraits of the following differential equations, seperately
x˙ = 1 − 2 cos x
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
Sulaymon Eshkabilov on 31 Oct 2021
Edited: Sulaymon Eshkabilov on 31 Oct 2021
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.