Non-linear growth business is best explained via examples. Twitter is a non-linear growth business because the number of users doubles every few months. Cellular service is a non-linear growth business because the number of cellular phone subscribers worldwide has doubled every year. Computer hardware is a non-linear growth business because the number of computers has doubled every few years and Moore's law has doubled the number of gates in a microprocessor every 2 years.
Naturally, such non-linear growth in a business attracts competition. For example, there are plenty of social networks vying for user attention and competing with Twitter. There is healthy competition in cellular service providers in most countries. Similarly, IBM has been supplanted in the PC hardware business by HP, Lenovo, Dell, etc. So the profit in a non-linear business can quickly evaporate due to competition. The pie is divided up. Capitalism and market forces 101.
But there are companies that build effective moats around their products and keep the whole pie. The moat is usually a combination of two components. One component is a standards and IPR protection for products. By creating a standardized and widely adopted product (e.g. MS Windows) companies can effectively keep others out. The second component is the high entry bar. A modern CISCO router ruitinely runs a 15-20m line operating system, making it incredibly hard for a start-up to join the fray.
CISCO operates on a pinchpoint, at the bottom of an inverted pyramid. At the top are all Web 2.0, Internet applications, and data centers. All the growth and innovation at the top makes money for CISCO. Intel is another pinchpoint and all PC manufactures compete at the top of the inverted pyramid. Truly smart are the business models that perch companies on the pinchpoints... the pie just keeps getting bigger!