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enter image description hereI am interested in solving this recurrence relation (equation) with Mathematica code. I am new to Mathematica. I tried RSolve, RSolveValue, AsymptoticRSolveValue commands for this. But I am not getting any result for different values of 'theta'. Any help would be highly appreciated. Thanks in advance.

RSolve[{a[n + 1] == \[Theta]*a[n] (-1 + a[n]), a[0] == 1}, a[n], n]
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    $\begingroup$ A nonlinear recurrence is not likely to have an explicit solution known to Mathematica. Of course, you can still use RecurrenceTable[] or the method in Akku's solution to generate the terms. $\endgroup$
    – J. M.'s lack of A.I. ♦
    Jul 8, 2020 at 12:32
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    $\begingroup$ Asymptotic solutions are a[n] = 0 and a[n] = 4/3. $\endgroup$
    – bbgodfrey
    Jul 9, 2020 at 1:51
  • $\begingroup$ Thank you for the suggestion. $\endgroup$
    – Shivam K
    Jul 10, 2020 at 18:31

1 Answer 1

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Define a recursion relation (with memorizing former values, which speeds up) like

a[0] = a0; 
a[n_] := a[n] = \[Theta]*a[n - 1] (-1 + a[n - 1])

a[3]

(*   (-1 + a0) a0 \[Theta]^3 (-1 + (-1 + a0) a0 \[Theta]) (-1 + (-1 + 
  a0) a0 \[Theta]^2 (-1 + (-1 + a0) a0 \[Theta]))   *)

But with a[0]=1, you get zero for n>0.

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  • $\begingroup$ Thank you very much. $\endgroup$
    – Shivam K
    Jul 10, 2020 at 18:29

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