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I have a set of data obtained by NDSolve. After I plot it, I want to indicate some feature of the curves. For example, I want to link the local minimum-value points between these curves by dotted line to highlight the track. First, I import the data:

data1 = Import["C:\\Users\\...\\Desktop\\data1.dat"];
data2 = Import["C:\\Users\\...\\Desktop\\data2.dat"];
data3 = Import["C:\\Users\\...\\Desktop\\data3.dat"];

then, plot them

g1 = ListLinePlot[data1];
g2 = ListLinePlot[data2];
g3 = ListLinePlot[data3];
Show[g1, g2, g3, PlotRange -> All]

I get the following plot

enter image description here

What I want to do is to link the local min-value point by dashed line. Is there any simply method by Mathematica to do this job? Should I make use of FindMinimum and FindMinValue, but I don't know how to combine them. The objective I want to obtain is as follows which is got by hand:). enter image description here

Yes, as answered by @Oska, whose code can handle many cases. But fail to treat the following case in which there are several local minimum-value points in a single curve. This is the my_data.

Using Oska's code

data1 = Import["C:\\...\\plot1_4sqrt(2)pi.dat"];
data2 = Import["C:\\...\\plot2_4sqrt(2)pi.dat"];
data3 = Import["C:\\...\\plot3_4sqrt(2)pi.dat"];

mins = Function[d, 
d[[#]] & /@ (Sort[
   First@First@
       Position[d, #] & /@ (RankedMin[Last /@ d, #] & /@ {1, 
       2})])] /@ {data1, data2, data3};
ListLinePlot[{data1, data2, data3}, 
Epilog -> {Arrowheads[0.02], 
Arrow /@ (Thread@{(First /@ mins), 
    RotateLeft@(First /@ mins)})[[;; -2]], 
Arrow /@ (Thread@{(Last /@ mins), 
    RotateLeft@(Last /@ mins)})[[;; -2]]}
]

I will get enter image description here

As can be seen, the code fails to find the local min-value points on the first curve. What I try to get is as follow. I am confusing that why the code can find the local min-value point of the other two curves but fails to the first curve? enter image description here

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  • $\begingroup$ You should consider doing a little bit of work and find the minima that you desire on your own. $\endgroup$ – Öskå Oct 16 '14 at 13:56
  • $\begingroup$ Yes, @Öskå. Thanks a LOT :). But could you give me some hints on why this code can not find the two local min-value points of the first curve but can find that of the other two similar curves. $\endgroup$ – Enter Oct 16 '14 at 14:42
  • $\begingroup$ You may consider searing on mathematica.SE: see here :) $\endgroup$ – Öskå Oct 16 '14 at 14:52
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I will let you play with the style but here is a beginning:

data1 = Import["~/Downloads/data/data1.dat"];
data2 = Import["~/Downloads/data/data2.dat"];
data3 = Import["~/Downloads/data/data3.dat"];
mins = Function[d, 
   d[[#]] & /@ (Sort[
      First@First@Position[d, #] & /@ (RankedMin[Last /@ d, #] & /@ {1, 2})])] /@ 
   {data1, data2, data3}

ListLinePlot[{data1, data2, data3}, 
 Epilog -> {Red, Line[First /@ mins], Line[Last /@ mins]}]

Mathematica graphics

Regarding the series of arrows:

ListLinePlot[{data1, data2, data3}, 
 Epilog -> {Red, 
   Arrow /@ (Thread@{(First /@ mins), RotateLeft@(First /@ mins)})[[;; -2]], 
   Arrow /@ (Thread@{(Last /@ mins), RotateLeft@(Last /@ mins)})[[;; -2]]},]

Mathematica graphics

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  • $\begingroup$ Thanks, @Oska! Is there any possible to add a series of arrows on the redline? I tried this code p0 = ListLinePlot[{data1, data2, data3}, Epilog -> {Red, Dashing[0.02], Line[First /@ mins], Line[Last /@ mins]}];p0 /. Line[x_] :> {Arrowheads[{0, .05, .05, 0}], Arrow[x]}. But I also added arrows on the three curve where I do not need arrow. $\endgroup$ – Enter Oct 16 '14 at 3:05
  • $\begingroup$ @lxy Please check the update :) $\endgroup$ – Öskå Oct 16 '14 at 10:09
  • $\begingroup$ Hi,@Oska,thank you for your helpful answer. But it might have a bug. I am confusing that why the code can find the local min-value point of the some curves but fails to the other curves? Could you pls see my post again which has been updated. Thank you for your time! $\endgroup$ – Enter Oct 16 '14 at 13:54

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