on 03-Sep-2022 (Sat)

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

To use the chart, analysts plot a scatter graph to rank the business units (or products) on the basis of their relative market shares and growth rates.

Cash cows is where a company has high market share in a slow-growing industry. These units typically generate cash in excess of the amount of cash needed to maintain the business. They are regarded as staid and boring, in a "mature" market, yet corporations value owning them due to their cash-generating qualities. They are to be "milked" continuously with as little investment as possible, since such investment would be wasted in an industry with low growth. Cash "milked" is used to fund stars and question marks, that are expected to become cash cows some time in the future.

Dogs, more charitably called pets, are units with low market share in a mature, slow-growing industry. These units typically "break even", generating barely enough cash to maintain the business's market share. Though owning a break-even unit provides the social benefit of providing jobs and possible synergies that assist other business units, from an accounting point of view such a unit is worthless, not generating cash for the company. They depress a profitable company's return on assets ratio, used by many investors to judge how well a company is being managed. Dogs, it is thought, should be sold off once short-time harvesting has been maximized.^[6]

Question marks (also known as a problem child or Wild dogs) are businesses operating with a low market share in a high-growth market. They are a starting point for most businesses. Question marks have a potential to gain market share and become stars, and eventually cash cows when market growth slows. If question marks do not succeed in becoming a market leader, then after perhaps years of cash consumption, they will degenerate into dogs when market growth declines. When shift from question mark to star is unlikely, the BCG matrix suggests divesting the question mark and repositioning its resources more effectively in the remainder of the corporate portfolio.^[6] Question marks must be analyzed carefully in order to determine whether they are worth the investment required to grow market share.

• Stars are units with a high market share in a fast-growing industry. They are graduated question marks with a market- or niche-leading trajectory, for example: amongst market share front-runners in a high-growth sector, and/or having a monopolistic or increasingly dominant unique selling proposition with burgeoning/fortuitous proposition drive(s) from: novelty, fashion/promotion (e.g. newly prestigious celebrity-branded fragrances), customer loyalty (e.g. greenfield or military/gang enforcement backed, and/or innovative, grey-market/illicit retail of addictive drugs, for instance the British East India Company's, late-1700s opium-based Qianlong Emperor embargo-busting, Canton System), goodwill (e.g. monopsonies) and/or gearing (e.g. oligopolies, for instance Portland cement producers near boomtowns),^{[ citation needed ]} etc. The hope is that stars become next cash cows.

Stars require high funding to fight competitors and maintain their growth rate. When industry growth slows, if they remain a niche leader or are amongst the market leaders, stars become cash cows; otherwise, they become dogs due to low relative market share.