Describe the solution trajectory of differential systems with mixed time-varying delay

Hi everyone, please help me write the matlab code to describe the solution trajectory for the class differential systems with mixed time-varying delay as follows

Thank you very much!

[Sam Chak]

Hi, it doesn't look like typical questions for typical Bachelor's degree students in the Differential Equations course. Equation 30 probably comes from a Journal Article or a Reference book.

If you believe this is a time dependent delay differential system, then try using the ddesd function finds the solution. Copy and modify the code from the example. Paste the code here and run it.

[Le]

Ok, thank you very much

Answer 1

[Torsten]

To write your equations as a system of delay differential equations that can be handled by a MATLAB solver, set

x3 = integral_{t-2-cos(2*t)}^{t} x1(s) ds

x4 = integral_{t-2-cos(2*t)}^{t} x2(s) ds

and differentiate x3 and x4 with respect to t using the Leibniz Integral Rule:

https://mathworld.wolfram.com/LeibnizIntegralRule.html

After this, you can use MATLAB's "ddesd" to solve for x1-x4:

https://uk.mathworks.com/help/matlab/ref/ddesd.html

[Le]

Thank you very much! Can you sent me a example of matlab code for type above differential system ?

[Torsten]

No, sorry, the hints I gave should suffice to set up the example without problems. If the code doesn't work, you can come back.

By the way: I set up the example from above and it works without changing any solver options.