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Help with NDSolve


[You may get two copies of this message. - moderator]

I am trying to solve a differential equation 
  NN'[t] = lambda ( 1 - B[t] ) - mu NN[t]
where B[t] is a fixed point of a function of NN[t] and B[t].

The program below does not, however, terminate.
It works if we use Nest instead of FixedPoint, but
we need FixedPoint for the stopping criteria.
I suspect that with FixedPoint Mathematica can not
symbolically get the differential equations.
Is there a way around this or it can't be done with
Mathematica ?

Any help is very much appreciated.

Best regards,
Ibrahim

=============================================

T = 20
lambda = 0.8 
mu = 1.0
K = 2

Clear[NN]
Clear[B]


B[b_] := (NN[t] / (1 - b))^K / K! / 
                        (1 + Sum[(NN[t] / (1 - b))^ii / ii!, {ii, K}])




 sol = NDSolve[{NN'[t] == 
        lambda (1 - FixedPoint[B, 0.1, SameTest->(Abs[#1 - #2] < 10.^-4 &)]) 
        - mu NN[t], NN[0] == 0}, 
                NN, {t, T}]

Plot[Evaluate[NN[t] /. sol], {t, 0, T}]

=============================================


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