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

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Le
Le 2024-5-26
评论： Torsten 2024-5-26
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!
  2 个评论
Sam Chak
Sam Chak 2024-5-26

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.

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Torsten
Torsten 2024-5-26
编辑：Torsten 2024-5-26
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
  2 个评论
Le
Le 2024-5-26
Thank you very much! Can you sent me a example of matlab code for type above differential system ?
Torsten
Torsten 2024-5-26
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.

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