Positive/negative feedback loops in natural processes
Positive/negative feedback loops that occur in nature fascinate me. So I started looking for them and collecting such phenomena. I'm not 100% sure if some of these are really due to the presence of positive/negative feedback loops -- so take it with a pinch of salt.
In simple terms, a positive feedback loop makes a thing larger and larger until a breaking point. The larger it gets, its tendency to get larger increases. The reverse of getting continuously smaller can also be the result of a positive feedback.
A negative feedback tends to resist a thing's current course of change. If it is growing, a negative feedback till tend to pull it back. So growing more becomes harder and harder as the thing grows big. Hence a negative feedback system normally has an equilibrium point. Any big swing away from the equilibrium will tend to pull the system back into its equilibrium.
Mathematically positive/negative feedback loop systems can be described as below. Note that I may not be 100% correct here. Let the thing that is growing/shrinking be y. If dy/dx is a polynomial in x and has a degree >= 1 (or <= -1 for shrinking positive feedback), we can say there is a positive feedback. In simpler terms, the rate at which the thing increases is directly proportional to the current size of the thing. Probably a more accurate description is that, the change in the thing (rather than the rate of change) is directly proportional to its current size. Imagine a forest fire. Larger the forest fire gets, the more rapidly it spreads. So we can say this is a case of positive feedback loop at work. I couldn't exactly quantify what x is; but intuitively it is something whose little change can dramatically affect y's change as y gets larger. Usually most spectacular phenomena (like a stock market boom/bust, current fashion craze) would have a positive feedback loop working for it. Here is a list of feedback loops I collected. I'll update as I come across interesting cases.
- Nuclear chain reaction, nuclear explosion
- Hurricane formation
- The growing crowd at a road side accident site. More watching people attract still more people. The reverse is also true -- a shrinking crowd, shrinks faster. As more people leave, it becomes less of a crowd puller.
- Anger bursts. This I read somewhere; the way human anger response works. Once it gets started, it keeps growing until it reaches a maximum point. I, for one, would bet on that theory having had first hand experiences :).
- Investment growth using compounding returns. Think of the growth of an initial investment in 401k over say 30 years.
- Popularity of already successful books/shows/ideas/etc. Usually people talk about book sales "taking off" or reaching "critical mass". It is when the book makes it to the top sellers list. I think this is a classic case of starting off of the positive feedback loop. There is no stopping of the runaway success.
- pumping and dumping of penny stocks. It is similar to the above case of book reaching the top seller list. Once a stock has been artificially pumped up (by a select few), others jump in pushing it further up. Again a start of a positive feedback loop.
- Stock market/ Real estate bubble build up. The reverse burst. Once an asset is seen growing more, more people want it. Higher demand drives value up. Again a start of a positive feedback loop. A crash in prices too gets into a positive feedback loop -- though here the effect is in making the value smaller and smaller.
- Trust/emotion building among people/groups. Includes cases of trust, love, hatred.
- Growth of a monopoly. Take Microsoft in late 80's, early 90's; or Walmart. In Microsoft, the explosive growth of windows can be seen as a result of positive feedback loop at work -- more apps for windows leads to more windows adoption. That triggers more developers to produce apps for windows (instead to say Linux or someother platform).
- Formation of black holes. More mass leads to heavier gravitational pull -- leading to more attraction of other mass. A cycle is established. It is an interesting comparison to see the way a monopoly works with this sucking effect of a black hole. Lets consider the introduction of a Walmart superstore in a community. It just sucks up all the mom-n-pop businesses and that leads to attracting their customers. Walmart just grows bigger in sales; now ready to swallow bigger guys -- I think the fall of Levis, RCA, rubbermaid to walmart can be seen as instances of such big guys falling.
- Population growth of self-reproducing entities. Includes all living things, computer virus, successful memes (like religion). For living things some examples are rabbit population, water hyacinth growth in a lake, cancer proliferation, biological epidemics (flu virus spread). The spread of successful ideas (memes) also employ positive feedback loops. More people exposed to an idea increases the chances of the idea spreading more rapidly. I guess gossips/rumors are a good example.
- Economic boom/depression. Similar to the stock market boom. More activity creates more jobs and a cycle gets established. The reverse happens in an economic downturn.
- Technology adoption. More technology adoption feeds innovation, leading to birth of newer smarter technology. Growth of Internet is an example.
- Drug addiction. Cocaine mimics the naturally occurring happiness hormone endorphin. On drug intake, the brain sees a sudden flood of endorphin like substance and shuts down the endorphin receptors. When the drug is digested, the person can no longer feel good since the naturally occurring endorphin is not sufficient enought to plug on to the available open receptors. He takes in more drug to achieve a prior state of well-being. That triggers closing down of still more receptors and reduces the available open ones. There starts the vicious cycle.
- Becoming obese: It's lot easier for an overweight person to add on more pounds -- bigger body demands more food. It also results in lesser exercise/physical activity. Both can setup a cycle. The good part is losing weight can also exploit the workings of a positive feedback loop. Once a few pounds are lost, it may need lesser effort to reduce further. There are many unknowns here and I may be off the mark.
- The classic spring example. It takes more and more effort to press/expand a spring from its natural equilibrium position.
- Steam power control in old steam locomotives. A valve opens/closes to regulate steam output based on the current steam power output. More power reduces the valve leading to power reduction. Less power opens up the value to increase power.
- Predator prey population. Think of lion-deer population. More lions implies reduction in deer population; that implies starvation for lions. This leads to an equilibrium state. Less lions implies population growth for deer leading to more food for lions helping their growth.
- Classic case of price stability due to supply-demand balance. Lets take oil price increase. Higher cost drives demand low (due to less driving, say) and that pulls back the price to an equilibrium state. The reverse happens when oil prices drop.
- Human body homeostasis. The body tries to maintain an equilibrium; lets take temperature. If too cold, the body shivers to bring up the temperature. If too warm, the body evaporates to cool down.