positive feedback

Positive feedback is a mechanism by which an output is enhanced. Here a molecular biology circuitry is used as an example is such as protein levels. [A]=k [A]

Positive feedback, sometimes referred to as "cumulative causation", is a feedback loop system in which the system responds to perturbation in the same direction as the perturbation. In contrast, a system that responds to the perturbation in the opposite direction is called a negative feedback system. These concepts were first recognized as broadly applicable by Norbert Wiener in his 1948 work on cybernetics.^[1]

Overview

A system in equilibrium in which there is positive feedback to any change in its current state is said to be in an unstable equilibrium, whereas it is possible for one with negative feedback to be in a stable equilibrium.

The end result of a positive feedback is often amplifying and "explosive," i.e. a small perturbation results in big changes. This feedback, in turn, will drive the system further away from its original set point, thus amplifying the original perturbation signal, and eventually become explosive because the amplification often grows exponentially (with the first order positive feedback), or even hyperbolically (with the second order positive feedback). Indeed, chemical and nuclear fission based explosives offer an excellent physical demonstration of positive feedback. Bombarding fissile material with neutrons causes it to emit even more neutrons, which in turn affect the material. The greater the mass of fissile material, the larger the amplification, resulting in greater feedback. If the amplification is great enough it becomes supercritical, the process accelerates until the fissile material is spent or dispersed by the resulting explosion.

Basic principles

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The effect of a positive feedback loop is not necessarily "positive" in the sense of being desirable. Positive refers to the direction of change rather than the desirability of the outcome. The negative feedback loop tends to reduce or inhibit a process, while the positive feedback loop tends to expand or promote it.

When a change in a variable occurs in a system, the system responds. In the case of positive feedback the response of the system is to change that variable even more in the same direction. A simple example in chemistry would be the phenomenon of autocatalysis, where a reaction is facilitated increasingly in the presence of its product. For another example, imagine an ecosystem with only one species and an unlimited amount of food. The population will grow at a rate proportional to the current population, which leads to an accelerating increase, i.e., positive feedback. This has a de-stabilizing effect, so left unchecked, does not result in homeostasis. In some cases (if not controlled by negative feedback), a positive feedback loop can run out of control, and can result in the collapse of the system. This is called vicious circle, or in Latin circulus vitiosus. People also refer to a virtuous circle, which is the same thing, but with an autocatalytic benign effect.

Consider a linear amplifier with linear feedback. As long as the loop gain, i.e. the forward gain multiplied with the feedback gain, is lower than 1 the result is a stable (convergent) output. This is also true for a negative feedback greater than -1. In electronic amplifiers the normal case is that the forward gain is quite high and the amplifier becomes unstable for quite small positive feedbacks.

In the real world, positive feedback loops are always controlled eventually by negative feedback of some sort; a microphone will break or a beaker will crack or a nuclear accident will result in meltdown. This outcome need not be so dramatic, however. The variety of negative feedback controls can modulate the effect. Embedded in a system of feedback loops, positive feedback does not necessarily imply a runaway process. Combined with other processes, it may just have an amplifying effect.

One common example of positive feedback is the network effect, where more people are encouraged to join a network the larger than network becomes. The result is that the network grows more and more quickly over time. This is the basis for many social phenomena, including the infamous Ponzi scheme. In this case, though, the population size is the limiting factor.

Applications

In biology

One example of a biological positive feedback loop is the onset of contractions in childbirth. 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.

Another example of a biological positive feedback loop 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.

Lactation involves positive feedback so that the more the baby suckles, the more milk is produced.

Estrogen that functions during the follicular phase of menstruation is also an example of positive feedback.

In most cases, once the purpose of the feedback loop is completed, counter-signals are released that suppress or break 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.

In electronics

Feedback is a process of sampling a part of the output signal, compounding it with some derived part of the source signal, and applying the compound to the input of the active feedforward element of the feedback loop. The input to the system as a whole comes from outside the system; it is energy derived from an external signal source, which is subject to leakage and noise on its way to and within the system, and within the system can be compounded with a sample from the output by way of the feedback element. The notion of feedback relies on the presence of a well defined loop around which signal power propagates, with a well-defined feedforward pathway inside the feedback loop, and in electronics this is achieved by use of active devices such as transistors or thermionic valves, which have access to a reservoir of power that they can tap to provide power gain for amplification. Feedback implies also the occurrence of a loop delay because that signal power propagation is causal. Negative feedback (patented by H.S. Black in 1934) is useful to set the parameters of an amplifier like voltage gain, input and output impedance, stability and bandwidth. On the other hand, positive feedback is rarely useful in amplifiers; it is useful only in very exceptional circumstances, one of which is to control the input impedance of the amplifier, and even then the amplifier is at serious risk of likely destructive instability.

Feedback is said to be positive if any increase in the output signal results in a feedback signal which on being compounded with a derivative of the source signal causes further increase in the magnitude of the output signal. Hence it is also called regenerative feedback. Positive feedback is in the same phase as the input signal, therefore the 'internal gain' of the amplifier (A_i) increases.

If the circuit elements are practically linear, the 'internal gain', A_i , of the feedback loop is given by A_i = (output voltage/input voltage) = A/ (1 − Aβ). Here A is the gain of the feedforward active part of the amplifier without feedback, and β is the gain of the feedback element. The 'loop gain' is Aβ. Final or amplifier gain refers to the relation between source signal and load quantity; as well as depending on the 'internal gain' of the feedback loop, the final amplifier gain depends also on the presence of leakage or 'parasitic' pathways, at the input, at the output, and as feedforward in parallel with the feedback loop, and it depends also on the load, which may be reactive.

An advantage here is the Swing-up control of an inverted pendulum on a cart. Disadvantages are:

• Gain can tend to be unstable
• Higher distortion
• Bandwidth decreases
• Stability is difficult or impossible to guarantee

Positive feedback is used extensively in oscillators and in regenerative radio receivers and Q multipliers.

The schmitt trigger circuit uses positive feedback to generate hysteresis and thus provide noise immunity on digital input.

Audio feedback or acoustic feedback is a common example of positive feedback. It is the familiar squeal that results when sound from loudspeakers enters a closely-placed microphone and gets amplified, and as a result the sound gets louder and louder. To avoid this condition, the microphone must be prevented from "hearing" its own loudspeaker.

In economics

In the World System development

The hyperbolic 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.

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^[2], 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.

Internet

Metaphorically, cumulative causation may emerge on the Internet as an echo chamber effect, which refers to any situation in which information or ideas are amplified by transmission inside an enclosed space. Another emerging term used to describe this "echoing" and homogenizing effect on the Internet within social communities is "cultural tribalism".

The Internet may be seen as a complex system (e.g., emergent, dynamic, evolutionary), and as such, will at times illuminate the effects of positive feedback loops (i.e., the echo-chamber effect) to that system, where a lack of perturbation to dimensions of the network, prohibits a sense of equilibrium to the system. Complex systems that are characterized by negative feedback loops will create more stability and balance during emergent and dynamic behaviour.

For example, observers of journalism in the mass media describe an echo chamber effect in media discourse. One purveyor of information will make a claim, which many like-minded people then repeat, overhear, and repeat again (often in an exaggerated or otherwise distorted form) until most people assume that some extreme variation of the story is true.

Due to this condition arising in online communities, participants may find their own opinions constantly echoed back to them, and in doing so reinforce a certain sense of truth that resonates with individual belief systems. This can create some significant challenges to critical discourse within an online medium. The echo-chamber effect may also impact a lack of recognition to large demographic changes in language and culture on the Internet if individuals only create, experience and navigate those online spaces that reinforce their "preferred" world view.

In computer games

World of Warcraft features a competitive multiplayer sub game called "arena"^[3]. It involves last man standing style gameplay in which teams fight each other in a confined environment. By repeatedly playing these mini games, the teams are rated in an Elo-like rating system. As a team increases its rating within the system, the players of the team gain access to better in-game equipment, that increases their chances to win in future arena games. Since increasing the team's rating indirectly increases the team's performance, the rating system has positive feedback, or more specifically, it exhibits the Matthew effect.

For example, a piece of equipment can have a minimum rating requirement of 1600. Suppose that a team rated at 1590 faces another team rated at 1610. The higher rated team will have access to the equipment that requires 1600 rating. Assuming that these two teams are identical in all other aspects, the higher rated team will be more likely to beat the lower rated team - not because it plays better, but because it happens to be above the required threshold for the improved equipment. As the higher rated team will win against the lower rated team more often than it will lose, assuming these teams only play each other the higher rated team will acquire higher rating, while the lower rated team will receive a lower rating.

This effect is also seen in browser games, leading to an effect known as "farming", where stronger players feed on weaker players, therefore increasing their advantages.

In climate

Examples in climate include:

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

On earth the gain is usually expected to be less than one stopping the system from suffering runaway effects. While there could be periods of time such as the exit from an ice age where the gain is greater than one, it hasn't been much greater than one nor lasted long enough for the oceans to boil away to create a situation like on Venus.

In sociology

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

See also

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

Analogous concepts

• Self-fulfilling prophecy
• Virtuous circle and vicious circle

Examples

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

References

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. Rles of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.