NSolve not solving within Table

Question

I would like to solve an equation for different parameter values, thus, I used Table[] to create an array of solutions. For some parameter combinations {k,A} NSolve does not give an answer, but when I call NSolve outside of Table with the same parameters, it actually works. Below is a minimal example of this behaviour - any ideas where this comes from are much appreciated :-). FYI I am using Mathematica 13.0 MacOS.

function[k_, A_, u1_, u2_] := (1 + Tanh[k (u1 - 2 A u2)])/2 - u1
results[k_, A_] := NSolve[function[k, A, u1, u2] == 0 && function[k, A, u2, u1] == 0 && 0 <= u1 <= 1 &&0 <= u2 <= 1, {u1, u2}]
{results[0.2, 2.2], results[0.2, 2.3], results[0.2, 2.4]}
Table[results[0.2, b], {b , 2.2, 2.4, 0.1}]

Follow up: Here are some more variations. It seems there is a difference between numbers explicitly typed in and those created automatically. When I type all numbers in Table, it works, but when I create a list of numbers with Range and use that in Table, it does not work anymore...

Table[results[0.2, b], {b, {2.2, 2.3, 2.4}}] // Quiet
values = Range[2.2, 2.4, 0.1];
Table[results[0.2, b], {b, values}] // Quiet

And similar issue with Map

Map[results[0.2, #] &, {2.2, 2.3, 2.4}] // Quiet
Map[results[0.2, #] &, values] // Quiet

Answer 1

Edit

Another way is use Rationalize to the values k and A

function[k_, A_, u1_, u2_] := (1 + Tanh[k (u1 - 2 A u2)])/2 - u1;
results[k_, A_] := 
 NSolve[function[Rationalize@k, Rationalize@A, u1, u2] == 0 && 
   function[Rationalize@k, Rationalize@A, u2, u1] == 0 && 
   0 <= u1 <= 1 && 0 <= u2 <= 1, {u1, u2}]
values = Range[2.2, 2.4, 0.1];
Table[results[0.2, b], {b, values}]
Table[results[0.2, b], {b, 2.2, 2.4, .1}]

Original

Maybe use exact number by Rationalize

values = Range[2.2, 2.4, 0.1] // Rationalize;
Table[results[0.2, b], {b, values}]

Answer 2

Try Map (don't know why Table doesn't work)

Map[results[0.2, #] &, { 2.2, 2.4, 0.1}] // Quiet
(*{{{u1 -> 0.375147, u2 -> 0.375147}}, 
{{u1 -> 0.364816,u2 -> 0.364816}}, 
{{u1 -> 0.54336, u2 -> 0.54336}}}*)

Edit I still do not understand why NSolve (numerical solver!) only evaluates with Rationalize!

NMinimize solves without this limitation:

res[k_, A_] := 
NMinimize[{1, function[k, A, u1, u2] == 0,function[k, A, u2, u1]== 0, 0 <= u1 <= 1, 0 <= u2 <= 1}, {u1, u2}] [[2]]

Table[res[0.2, b], {b, {2.2, 2.4, .1}}]
(*{{u1 -> 0.375147, u2 -> 0.375147}, {u1 -> 0.364816,u2 -> 0.364816}, {u1 -> 0.54336, u2 -> 0.54336}}*)