# Strange Recursion with non-constant coefficient

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 $$1$$.

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