Timeline for Local optimization of parameters in a Coupled Non-Linear System
Current License: CC BY-SA 3.0
24 events
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| Jan 27, 2017 at 15:06 | vote | accept | Aritra Saha | ||
| Jan 27, 2017 at 14:51 | answer | added | gpap | timeline score: 3 | |
| Jan 27, 2017 at 13:44 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 27, 2017 at 13:28 | comment | added | Aritra Saha | Yes you are absolutely correct @gpap. I have reworked the question again. Thanks for pointing out an erroneous concept. | |
| Jan 27, 2017 at 13:27 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 26, 2017 at 16:02 | history | tweeted | twitter.com/StackMma/status/824648684503781378 | ||
| Jan 26, 2017 at 14:38 | comment | added | gpap |
I still think this question doesn't make sense. There is no one combination of $c_i$ that gives you the lower or higher envelope of the solution as each differential equation solved (for each collection of parameters) results in solution that oscillates with different frequency so the solutions cross each other. Consider this code Plot[Evaluate@({x[1, 0, 0, 1][t], x[0, 1, 1, 1][t], x[0, 0, 0, 0][t]} /. sol), {t, 0, 25}]. Which is the "lower bound" of these three curves? The first, second or third? Your answer depends on which time scale you look at.
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| Jan 26, 2017 at 12:48 | comment | added | Aritra Saha | I apologise for the mismatch. Added the plot commands too. @bbgodfrey | |
| Jan 26, 2017 at 12:46 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 25, 2017 at 20:56 | comment | added | bbgodfrey | Not all the constants in the LaTeX version of the equations are the same as those in the Mathematica version of the equations. Please edit to make them consistent. Also, please add the code you used to plot the functions. Thanks. | |
| Jan 25, 2017 at 19:05 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 25, 2017 at 17:18 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 25, 2017 at 16:42 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
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| Jan 24, 2017 at 17:27 | history | edited | J. M.'s missing motivation♦ |
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| Jan 24, 2017 at 17:25 | comment | added | Aritra Saha |
That is why tried the NMinimize command on $X(t)$ and $Y(t)$ separately. It may be possible that the $c_{i}$ are different. In that case, I want both of them in my output.
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| Jan 24, 2017 at 17:20 | comment | added | J. M.'s missing motivation♦ | It is possible that the $c_i$ that maximize $\|X(t)\|_\infty$ can be different from the $c_i$ that maximize $\|Y(t)\|_\infty$; what do you propose to do in that case? | |
| Jan 24, 2017 at 17:16 | comment | added | Aritra Saha | Yes. And I want to know the values of $c_{i}$ at which the maximum and minimum occur. I did it for discrete values, but I have no idea about how to do it over a specified interval. | |
| Jan 24, 2017 at 17:14 | comment | added | J. M.'s missing motivation♦ | In short, you effectively want to maximize $\|X(t)\|_\infty$ and $\|Y(t)\|_\infty$ in the "upper envelope" case? | |
| Jan 24, 2017 at 17:13 | comment | added | Aritra Saha | By "small" and "big" I mean the combination of $c_{i}$ which will give the topmost solution. The blue line represents the lower solution, but I do not know which combination of $c_{i}$ produced it. | |
| Jan 24, 2017 at 17:04 | comment | added | gpap | How can a time-varying oscillating solution be "small"? Isn't this the lower bounds (blue) curves that you are showing on the plots? | |
| Jan 24, 2017 at 16:59 | comment | added | Aritra Saha | The solution of the coupled equation. $X(t)$ and $Y(t)$ in this case. | |
| Jan 24, 2017 at 16:58 | history | edited | Aritra Saha | CC BY-SA 3.0 |
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| Jan 24, 2017 at 16:53 | comment | added | J. M.'s missing motivation♦ | Any optimization does require that you construct a merit function; that is, what exactly are you optimizing? What should be "big", and what should be "small"? | |
| Jan 24, 2017 at 16:48 | history | asked | Aritra Saha | CC BY-SA 3.0 |