  An extension of the nonlinear feedback (NLF) formalism to describe regimes of
hyper- and high-inflation in economy is proposed in the present work. In the
NLF model the consumer price index (CPI) exhibits a finite time singularity of
the type $1/(t_c -t)^{(1- \beta)/\beta}$, with $\beta>0$, predicting a blow up
of the economy at a critical time $t_c$. However, this model fails in
determining $t_c$ in the case of weak hyperinflation regimes like, e.g., that
occurred in Israel. To overcome this trouble, the NLF model is extended by
introducing a parameter $\gamma$, which multiplies all therms with past growth
rate index (GRI). In this novel approach the solution for CPI is also analytic
being proportional to the Gaussian hypergeometric function
$_2F_1(1/\beta,1/\beta,1+1/\beta;z)$, where $z$ is a function of $\beta$,
$\gamma$, and $t_c$. For $z \to 1$ this hypergeometric function diverges
leading to a finite time singularity, from which a value of $t_c$ can be
determined. This singularity is also present in GRI. It is shown that the
interplay between parameters $\beta$ and $\gamma$ may produce phenomena of
multiple equilibria. An analysis of the severe hyperinflation occurred in
Hungary proves that the novel model is robust. When this model is used for
examining data of Israel a reasonable $t_c$ is got. High-inflation regimes in
Mexico and Iceland, which exhibit weaker inflations than that of Israel, are
also successfully described.
