Actually growth patterns of animals vary wildly. There's a whole set of animals that get "unstable" growth - Cats are famous for this, for example. That means that cat numbers in specific areas actually grow to the point that cats die out in the next generation, destabilizing the entire food chain in the process (happened in Australia, for example)

The problem with this instability is that the numbers bounce around wildly. Up and down, by a lot, in as little as 2 or 3 generations. But there's a process that stops the bouncing: hitting zero.

Cats are kind of crazy as an invasive predator: they can be sexually mature after 6 months and have litters of up to 6 kittens every 3 months.

Obviously that's more at the upper end, but for an obligate carnivore that is an amazing multiplier.