Positive feedback

Alarm or panic can spread by positive feedback among a herd of animals to cause a stampede.

Positive feedback is energy taken from the output of a system and reapplied to the input, which is phase-congruent with the input signal.

A system exhibiting positive feedback, in response to perturbation, acts to increase the magnitude of the perturbation, unless the feedback loop is controlled by being clamped, dampened, gated, channel-limited, or otherwise physically limited. Uncontrolled systems exhibiting positive feedback often result in an explosive release of energy, the result of which is to move the system towards a more stable state. This typically results in physical deformation of the system.

Positive feedback occurs when A produces more of B which in turn produces more of A.^[1] In contrast, a system that responds to a perturbation in a way that reduces its effect is said to exhibit negative feedback. These concepts were first recognized as broadly applicable by Norbert Wiener in his 1948 work on cybernetics.^[2]

Positive feedback often leads to exponential divergences or the exponential growth of oscillations. Under positive feedback and a lack of stabilizing forces, systems will typically accelerate towards a non-linear region, which may stabilise the system or, conversely, destroy it. Positive feedback may end with the system 'latched' into a new stable state.

In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. See also viral video.

Unintended positive feedback may not be "positive" in the sense of being desirable. Positive refers to the direction of change rather than the desirability of the outcome. To avoid this confusion, it is sometimes better to use other terms such as self-reinforcing feedback.^[3] In social and financial systems, positive feedback effects may also be referred to as 'virtuous' or 'vicious' circles.

Positive feedback is used in digital electronics to force voltages away from intermediate voltages into '0' and '1' states. On the other hand, thermal runaway is a positive feedback that can destroy semiconductor junctions. Positive feedback in chemical reactions can increase the rate of reactions, and in some cases can lead to explosions. Positive feedback in mechanical design causes tipping-point, or 'over-centre', mechanisms to snap into position, for example in switches and locking pliers. Out of control, it can cause bridges to collapse. Positive feedback in economic systems can cause boom-then-bust cycles.

Overview

The key feature of positive feedback is that small disturbances are amplified. When positive feedback is present, there is some causal loop where a small change creates an effect that causes an even bigger change, like a ball rolling down an increasingly steep hill.

When a change in a variable occurs in a system which exhibits positive feedback, the system responds by changing that variable even more in the same direction.

The end result of positive feedback is to amplify so that small perturbations may result in big changes. For example, if a chemical reaction causes the release of heat, and the reaction itself happens faster at higher temperatures, then there is a high likelihood of positive feedback. If the heat produced is not removed from the reactants fast enough, thermal runaway can occur and very quickly lead to a chemical explosion. Equally, if a PA system microphone picks up sounds from its own loudspeakers and these sounds are re-amplified enough, the effect can be loud squealing or howling noises from the loudspeakers.

Formally, a system in equilibrium in which there is positive feedback to any change from its current state is said to be in an unstable equilibrium. The magnitude of the forces which act to move such a system away from its set point are an increasing function of the "distance" from the set point.

In the real world, positive feedback loops are always controlled eventually by negative feedback or limiting effects of some sort. Acoustic feedback causes a PA system to reach its maximum volume and so it cannot amplify any further; a flask may crack and the chemical reactants spray into the air or spill onto the floor, where they spread out and cool. Negative feedback effects within the same system can also modulate the effect of positive feedback so that it may add to the responsiveness of the system but does not necessarily lead to a runaway process.

Examples and Applications

In Biology

Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A]

In biology, a number of examples of positive feedback systems may be found in physiology, some of which are well described in works such as Arthur Guyton's 'Textbook of Medical Physiology'.^[4]

• One example is the onset of contractions in childbirth, known as the Ferguson reflex. When a contraction occurs, the hormone oxytocin is released into the body, which stimulates further contractions. This results in contractions increasing in amplitude and frequency.^[5]

• Another example is the process of blood clotting. The loop is initiated when injured tissue releases signal chemicals that activate platelets in the blood. An activated platelet releases chemicals to activate more platelets, causing a rapid cascade and the formation of a blood clot.^[6]

• Lactation also involves positive feedback in that the more the baby sucks, the more milk is produced, via a surge in prolactin secretion.^[7]

• Estrogen that functions during the follicular phase of menstruation is also an example of positive feedback.^[8]

• The generation of nerve signals is another example, in which the membrane of a nerve fibre causes slight leakage of sodium ions through sodium channels, resulting in a change in the membrane potential, which in turn causes more opening of channels, and so on. So a slight initial leakage results in an explosion of sodium leakage which creates the nerve action potential.^[9]

In most cases, such feedback loops culminate in counter-signals being released that suppress or breaks the loop. Childbirth contractions stop when the baby is out of the mother's body. Chemicals break down the blood clot. Lactation stops when the baby no longer nurses.^[4]

The analogy of Evolutionary arms races provide further examples of positive feedback in biological systems.^[10] While analogies used to describe, theorise, or explicate evolutionary positive feedback are considered by some as an adaptive process, the essential feature of positive feedback is that of the process itself, namely cumulative causation and amplification, as outlined further above. This is unrelated to what people want to believe about it (for example that it must be progressive), or whether they like the outcome which can be favourable or unfavourable. Thus it is "a means of conceptualising the adaptive or maladaptive consequences of given processes or actions".^[11]

Positive feedback loops have been utilised in several adaptive theories and explanations pertaining to human evolution and performance. For example, beginning at the macro level, Alfred J. Lotka (1945) argued that the evolution of the species was most essentially a matter of selection that fed back energy flows to capture more and more energy for use by living systems.^[12] At the human level, Richard Alexander (1989) proposed that social competition between and within human groups fed back to the selection of intelligence thus constantly producing more and more refined human intelligence.^[13] Since humans have collectively evolved to be capable of capturing and using more energy that any other species, Lotka’s rigorous energy model of positive feedback and Alexander’s social model of positive feedback appear to be in mutually supportive agreement. Crespi (2004) discussed several other examples of positive feedback loops in evolution.^[14] In psychology, Winner (1996) described gifted children, perhaps representative of the highest class of human intelligence, as driven by positive feedback loops involving setting their own learning course, this feeding back satisfaction, thus further setting their learning goals to higher levels and so on.^[15] Winner termed this positive feedback loop as a “rage to master.” Vandervert (2009a, 2009b) proposed that the child prodigy (a gifted child who reaches adult status in a particular domain of learning, for example, mathematics, music or art by age 10) can be explained in terms of a positive feedback loop between the output of thinking/performing in working memory, which then is fed to the cerebellum where it is streamlined, and then fed back to working memory thus steadily increasing the quantitative and qualitative output of working memory.^[16][17] Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for language evolution in working memory.

During the Phanerozoic the biodiversity shows a steady but not monotonic increase from near zero to several thousands of genera.

It have been shown that changes in biodiversity through the Phanerozoic correlate much better with hyperbolic model (widely used in demography and macrosociology) than with exponential and logistic models (traditionally used in population biology and extensively applied to fossil biodiversity as well). The latter models imply that changes in diversity are guided by a first-order positive feedback (more ancestors, more descendants) and/or a negative feedback arising from resource limitation. Hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the world population growth has been demonstrated (see below) to arise from a second-order positive feedback between the population size and the rate of technological growth. The hyperbolic character of biodiversity growth can be similarly accounted for by a positive feedback between the diversity and community structure complexity. It has been suggested that the similarity between the curves of biodiversity and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend (produced by the positive feedback) with cyclical and stochastic dynamics.^[18]

In electronics

Electronic amplification devices may have positive feedback signal paths intentionally added, or such paths may come into being inadvertently. In addition, thermal positive feedback may take place in electronic circuits. This is called thermal runaway and can be destructive.

In networking, a form of positive feedback known as a broadcast storm can result when multiple switches are connected in such a way that they form a loop. Say for example, you have two switches, each with 4 ports. By accident, ports 1 and 2 are connected to the other switches ports 1 and 2. A single multi-cast packet is sent, switch one receives it, and sends it out through every port besides the one it came in on. Switch 2 receives 2 multi-casts, and sends each of them out on every port besides the ones they came in on. Switch 1 then receives 2 again, and the process repeats. This begins flooding the network with packets being rapidly bounced back and forth until the entire network is crippled.

A vintage style regenerative radio receiver. Note how, due to the controlled use of positive feedback, sufficient amplification can be derived from a single vacuum tube or valve (centre).

Regenerative circuits were invented and patented in 1914^[19] for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single transistor amplifier can multiply its gain by 1,000 or more.^[20] Therefore a signal can be amplified 20,000 or even 100,000 times in one stage, that would normally have a gain of only 20 to 50. The problem with regenerative amplifiers working at these very high gains is that they easily become unstable and start to oscillate. The radio operator has to be prepared to tweak the amount of feedback fairly continuously for good reception. Modern radio receivers use the superheterodyne design, with many more amplification stages, but much more stable operation and no positive feedback.

The oscillation that can break out in a regenerative radio circuit can be put to good use in the design of electronic oscillators. By the use of tuned circuits or a piezoelectric crystal (commonly quartz), the signal that is amplified by the positive feedback remains linear and sinusoidal. There are several designs for such harmonic oscillators, including the Armstrong oscillator, hartley oscillator, colpitts oscillator, and the wien bridge oscillator. They all use positive feedback to maintain the oscillations.^[21]

Many electronic circuits, especially amplifiers, incorporate negative feedback. This reduces their gain, but improves their input impedance, output impedance, and bandwidth, and stabilises all of these parameters, including the closed-loop gain. These parameters also become less dependent on the details of the amplifying device itself, and more dependent on the feedback components, which are less likely to vary with manufacturing tolerance, age and temperature. The difference between positive and negative feedback for AC signals is one of phase: if the signal is fed back out of phase, the feedback is negative and if it is in-phase the feedback is positive. One problem for amplifier designers who use negative feedback is that some of the components of the circuit will introduce phase shift in the feedback path. If there is a frequency (usually a high frequency) where the phase shift reaches 180°, then the designer must ensure that the amplifier gain at that frequency is very low (usually by low-pass filtering). If the loop gain (the product of the amplifier gain and the extent of the positive feedback) at any frequency is greater than one, then the amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations. An amplifier that is stable in one set of conditions can break into parasitic oscillation in another. This may be due to changes in temperature, supply voltage, adjustment of front-panel controls, or even the proximity of a person or other conductive item. Amplifiers may oscillate gently in ways that are hard to detect without an oscilloscope, or the oscillations may be so extensive that only a very distorted or no required signal at all gets through, or that damage occurs. Low frequency parasitic oscillations have been called 'motorboating' due to the similarity to the sound of a low-revving exhaust note.^[22]

The effect of using a Schmitt trigger (B) instead of a comparator (A)

Digital electronic circuits are sometimes designed to benefit from positive feedback. Normal logic gates usually rely simply on gain to push digital signal voltages away from intermediate values to the values that are meant to represent boolean '0' and '1'. When an input voltage is expected to vary in an analogue way, but sharp thresholds are required for later digital processing, the Schmitt trigger circuit uses positive feedback to ensure that if the input voltage creeps gently above the threshold, the output is forced smartly and rapidly from one logic state to the other. One of the corollaries of the Schmitt trigger's use of positive feedback is that, should the input voltage move gently down again past the same threshold, the positive feedback will hold the output in the same state with no change. This effect is called hysteresis: the input voltage has to drop past a different, lower threshold to 'un-latch' the output and reset it to its original digital value. By reducing the extent of the positive feedback, the hysteresis-width can be reduced, but it can not entirely be eradicated. The Schmitt trigger is, to some extent, a latching circuit.^[23]

Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively.

An electronic latch is a circuit that has the effect of memory. For example, a Schmitt trigger circuit in a stable state, with an input voltage between its two threshold levels, in the middle of its hysteresis band, can tell the observer whether the last input swing it saw was higher or lower than the outer edges of its hysteresis band. This is the basis of one bit of electronic memory. The actual memory circuits used in most digital electronics are based on the 'flip-flop' or 'bistable multivibrator'. A bistable multivibrator uses logic gates connected to each other so that positive feedback maintains the state of the circuit after the input signal has been removed, until a suitable alternative signal is applied to change the state.^[24] This is usually a form of volatile memory, in the sense that removing power from the flip-flop circuit will usually cause it to lose state. Computer random access memory (RAM) can be made in this way, with one latching circuit for each bit of memory, eight to the byte.^[25]

Thermal runaway occurs in electronic systems because some aspect of a circuit is allowed to pass more current when it gets hotter, then the hotter it gets, the more current it passes, which, directly or indirectly, makes it pass yet more current. The effects are usually catastrophic for the device in question. If devices have to be used near to their maximum power-handling capacity, and thermal runaway is possible or likely under certain conditions, improvements can usually be achieved by careful design.^[26]

A phonograph turntable is prone to acoustic feedback

Audio and video systems can easily be made to demonstrate positive feedback. If a microphone picks up the amplified sound loudspeakers in the same circuit, then howling and screeching sounds of audio feedback (at up to the maximum power capacity of the amplifier) will be heard, as random noise is re-amplified by positive feedback and filtered by the characteristics of the audio system and the room. Microphones are not the only transducers subject to this effect. Phonograph turntables are also prone to picking up acoustic feedback, usually in the low frequency range < 100Hz, manifesting as a low rumble. Usually moving the placement or orientation (due to the directional nature of all transducers) of the mic, turntable, or speakers is the cure for this, although using EQ can help if the system tends to be resonant mostly in certain bands. This resonance is due to acoustical characteristics of the room and nature of electrical circuits.

Video feedback.

Similarly, if a video camera is pointed at a monitor screen that is displaying the camera's own signal, then weird repeating patterns can be formed on the screen by positive feedback. This video feedback effect was used in the opening sequences to early series of the television programme Dr Who. Jimi Hendrix helped to develop the controlled and musical use of audio feedback in electric guitar playing,^[27] and later Brian May was a famous proponent of the technique.^[28]

In economics

In the World System development

The exponential growth of the world population observed until the 1970s has recently been correlated to a non-linear second order positive feedback between the demographic growth and technological development that can be spelled out as follows: technological growth - increase in the carrying capacity of land for people - demographic growth - more people - more potential inventors - acceleration of technological growth - accelerating growth of the carrying capacity - the faster population growth - accelerating growth of the number of potential inventors - faster technological growth - hence, the faster growth of the Earth's carrying capacity for people, and so on (see, e.g., Introduction to Social Macrodynamics by Andrey Korotayev et al.).

Systemic risk

Systemic risk is the risk that an amplification or leverage or positive feedback process is built into a system, this is usually unknown, and under certain conditions this process can amplify exponentially and rapidly lead to destructive or chaotic behavior. A Ponzi scheme is a good example of a positive-feedback system, because its output (profit) is fed back to the input (new investors), causing rapid growth toward collapse. W. Brian Arthur has also studied and written on positive feedback in the economy (e.g. W. Brian Arthur, 1990)^[29]

Simple systems that clearly separate the inputs from the outputs are not prone to systemic risk. This risk is more likely as the complexity of the system increases, because it becomes more difficult to see or analyze all the possible combinations of variables in the system even under careful stress testing conditions. The more efficient a complex system is, the more likely it is to be prone to systemic risks, because it takes only a small amount of deviation to disrupt the system. Therefore well-designed complex systems generally have built-in features to avoid this condition, such as a small amount of friction, or resistance, or inertia, or time delay to decouple the outputs from the inputs within the system. These factors amount to an inefficiency, but they are necessary to avoid instabilities.

Population and agriculture

Agriculture and human population can be considered to be in a positive feedback mode,^[30] which means that one drives the other with increasing intensity. It is suggested that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and is resorting to highly-efficient monocultures which are more susceptible to systemic risk.

In climatology

See also: Climate change feedback

Within climate, it is important to remember that a positive feedback subsystem never acts in isolation, but is always embedded within the overall climate system, which itself is always subject to a very powerful negative feedback, the Stefan–Boltzmann law: that emitted radiation rises with the fourth power of temperature. Hence, on earth the gain of the overall system is always less than one, stopping the system from suffering runaway effects. While there may have been periods of time such as the exit from an ice age where the gain was greater than one, this has not lasted long enough for extreme effects such as the evaporation of the oceans as is believed to have happened on Venus.

Examples of positive feedback subsystems in climatology include:

• A warmer atmosphere will melt ice and this changes the albedo which further warms the atmosphere.
• Methane hydrates can be unstable so that a warming ocean could release more methane, which is also a greenhouse gas.

In sociology

A self-fulfilling prophecy is a social positive feedback loop between beliefs and behavior: if enough people believe that something is true, their behavior can make it true, and observations of their behavior may turn increase belief. A classic example is a bank run.

Another sociological example of positive feedback is the network effect. When more people are encouraged to join a network this increases the reach of the network therefore the network expands ever more quickly. A viral video is an example of the network effect in which links to a popular video are shared and redistributed, ensuring that more people see the video and then re-publish the links. This is the basis for many social phenomena, including Ponzi schemes and chain letters. In many cases population size is the limiting factor to the feedback effect.

See also

• Chain reaction
• Donella Meadows' twelve leverage points to intervene in a system
• Greenhouse effect
• Hyperbolic growth
• Reflexivity (social theory)
• Strategic complementarity
• Stability criterion
• System dynamics
• Technological Singularity
• Thermal runaway
• Negative feedback

Analogous concepts

• Self-fulfilling prophecy
• Virtuous circle and vicious circle
• Matthew effect (sociology)
• Matthew effect (education)
• Law of Attraction
• Karma

Examples

• Bus bunching
• Cytokine storm
• Matthew effect
• Autocatalysis
• Meander
• Runaway greenhouse effect
• Larsen effect

References

1. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.
2. ^ Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.
3. ^ Peter M. Senge (1990). The Fifth Discipline: The Art and Practice of the Learning Organization. New York: Doubleday. pp. 424. ISBN 0-385-260-946. 
4. ^ ^{a b} Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1
5. ^ Guyton, Arthur C. (1991), pp.924-925.
6. ^ Guyton, Arthur C. (1991), pp.392-394.
7. ^ Guyton, Arthur C. (1991), p.926.
8. ^ Guyton, Arthur C. (1991), p.907.
9. ^ Guyton, Arthur C. (1991), p.59.
10. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand
11. ^ Seymour-Smith, Charlotte (1990). Macmillan Dictionary of Anthropology. London: Macmillan Press. p. 114. ISBN 0-333-39334-1. 
12. ^ Lotka, A. (1945). The law of evolution as a maximal principle. Human Biology, 17, 168-194.
13. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.
14. ^ Crespi B. J. (2004) Vicious circles: positive feedback in major evolutionary and ecological transitions. Trends in Ecology and Evolution, 19, 627-633.
15. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books.
16. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.
17. ^ Vandervert, L. (2009b). The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation. The Journal of Mind and Behavior, 30, 15-32.
18. ^ Markov A., Korotayev A.Phanerozoic marine biodiversity follows a hyperbolic trend // Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318; Markov A., Korotayev A. Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution // Journal of General Biology. Volume 69, 2008. N 3, pp. 175–194.
19. ^ Armstrong, E. H., U.S. Patent 1,113,149, Wireless receiving system, 1914.
20. ^ Kitchin, Charles. "A SHORT WAVE REGENERATIVE RECEIVER PROJECT". http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm. Retrieved 23 September 2010. 
21. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. http://www.educypedia.be/electronics/analogosciltypes.htm. Retrieved 23 September 2010. 
22. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0240521626. http://books.google.com/books?id=Qpmi4ia2nhcC&pg=PA254&lpg=PA254#v=onepage&q&f=false. 
23. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component". Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. http://www.fairchildsemi.com/an/AN/AN-140.pdf. Retrieved 29 September 2010. 
24. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. http://www.labri.fr/perso/strandh/Teaching/AMP/Common/Strandh-Tutorial/flip-flops.html. Retrieved 4 November 2010. 
25. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. http://www.electronics-tutorials.ws/sequential/seq_1.html. Retrieved 29 September 2010. 
26. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". http://cnx.org/content/m31058/latest/. Retrieved 29 September 2010. 
27. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 0879307641. 
28. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. http://www.brianmayguitars.co.uk/accessories/19. Retrieved 2 February 2011. 
29. ^ W. Brian Arthur (February 1990). "Positive Feedbacks in the Economy". Scientific American, Vol 262. No.2, p.80
30. ^ Brown, A. Duncan. (2003) [1] Feed or Feedback. Publisher: International Books.

Further reading

• Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.
• Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.