Hyperbolic growth

is infinite: any similar graph is said to exhibit hyperbolic growth.

In the real world hyperbolic growth is created by certain non-linear positive feedback mechanisms.

These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior as input gets large) differs dramatically: Certain mathematical models suggest that until the early 1970s the world population underwent hyperbolic growth (see, e.g., Introduction to Social Macrodynamics by Andrey Korotayev et al.).

It was also shown that until the 1970s the hyperbolic growth of the world population was accompanied by quadratic-hyperbolic growth of the world GDP, and developed a number of mathematical models describing both this phenomenon, and the World System withdrawal from the blow-up regime observed in the recent decades.

[3] It has been also demonstrated that the hyperbolic models of this type may be used to describe in a rather accurate way the overall growth of the planetary complexity of the Earth since 4 billion BC up to the present.

Another example of hyperbolic growth can be found in queueing theory: the average waiting time of randomly arriving customers grows hyperbolically as a function of the average load ratio of the server.

If the processing needs exceed the server's capacity, then there is no well-defined average waiting time, as the queue can grow without bound.

A practical implication of this particular example is that for highly loaded queuing systems the average waiting time can be extremely sensitive to the processing capacity.

The function exhibits hyperbolic growth with a singularity at time