I try to analyze the following recursion but I do not really now the tools for analyzing recursions with non-constant coefficients.

Can anyone give me a hint?

$c$ is a constant between $0$ and $1$.

$x(t) = \frac{x(t-1)}{2\cdot \sqrt{c^2 + x(t-1)^2)}}+ \frac{1}{2}x(t-1)$

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