Positive Feedback Loop

Explanation

Positive feedback is a process that occurs in a feedback loop in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, mechanism A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it, has negative feedback (see: Negative Feedback Loop).

Figure: Positive feedback loop.

Mathematically, positive feedback is defined as a positive loop gain around a closed loop of cause and effect. That is, positive feedback is in phase with the input, in the sense that it adds to make the input larger. Positive feedback tends to cause system instability. When the loop gain is positive and above 1, there will typically be exponential growth, increasing oscillations or divergences from equilibrium. System parameters will typically accelerate towards extreme values, which may damage or destroy the system, or may end with the system latched into a new stable state. Positive feedback may be controlled by signals in the system being filtered, damped, or limited, or it can be cancelled or reduced by adding negative feedback.

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. A familiar example of positive feedback is the loud squealing or howling sound produced by audio feedback in public address systems: the microphone picks up sound from its own loudspeakers, amplifies it, and sends it through the speakers again.

In place of the adjective "Positive", alternative terms are used, such as: regenerative, self-stimulating, self-reinforcing, self-amplifying, discrepancy-increasing, or centrifugal.

Figure: Possible results of a Positive feedback loop.

Overview

Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it. For example, when part of an electronic output signal returns to the input, and is in phase with it, the system gain is increased. The feedback from the outcome to the originating process can be direct, or it can be via other state variables. Such systems can give rich qualitative behaviours, but whether the feedback is instantaneously positive or negative in sign has an extremely important influence on the results. Positive feedback reinforces and negative feedback moderates the original process. Positive and negative in this sense refer to loop gains greater than or less than zero, and do not imply any value judgements as to the desirability of the outcomes or effects. A key feature of positive feedback is thus that small disturbances get bigger. When a change occurs in a system, positive feedback causes further change, in the same direction.

If the loop gain AB is positive, then a condition of positive or regenerative feedback exists. Thus depending on the feedback, state changes can be convergent, or divergent. The result of positive feedback is to augment changes, so that small perturbations may result in big changes.

In the real world, positive feedback loops typically do not cause ever-increasing growth, but are modified by limiting effects of some sort. According to Donella Meadows: "Positive feedback loops are sources of growth, explosion, erosion, and collapse in systems. A system with an unchecked positive loop ultimately will destroy itself. That’s why there are so few of them. Usually a negative loop will kick in sooner or later."

Fields of application

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] .

Physiology

A number of examples of positive feedback systems may be found in physiology. One example is the onset of contractions in childbirth, known as the Ferguson reflex. When a contraction occurs, the hormone oxytocin causes a nerve stimulus, which stimulates the hypothalamus to produce more oxytocin, which increases uterine contractions. This results in contractions increasing in amplitude and frequency.

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.

Lactation also involves positive feedback in that as the baby suckles on the nipple there is a nerve response into the spinal cord and up into the hypothalamus of the brain. The hypothalamus then stimulates the pituitary gland to produce more prolactin to produce more milk.

A spike in estrogen during the follicular phase of the menstrual cycle causes ovulation.

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. This results 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.

In excitation–contraction coupling of the heart, an increase in intracellular calcium ions to the cardiac myocyte is detected by ryanodine receptors in the membrane of the sarcoplasmic reticulum. These ryanodine receptors transport calcium out into the cytosol in a positive feedback physiological response.

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.

Gene regulation

Positive feedback is a well studied phenomenon in gene regulation, where it is most often associated with bistability. Positive feedback occurs when a gene activates itself directly or indirectly via a double negative feedback loop. Genetic engineers have constructed and tested simple positive feedback networks in bacteria to demonstrate the concept of bistability. A classic example of positive feedback is the lac operon in Escherichia coli. Positive feedback plays an integral role in cellular differentiation, development, and cancer progression, and therefore, positive feedback in gene regulation can have significant physiological consequences. Random motions in molecular dynamics coupled with positive feedback can trigger interesting effects, such as create population of phenotypically different cells from the same parent cell. This happens because noise can become amplified by positive feedback. Positive feedback can also occur in other forms of cell signaling, such as enzyme kinetics or metabolic pathways.

Evolutionary biology

Positive feedback loops have been used to describe aspects of the dynamics of change in biological evolution. 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. 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. Crespi (2004) discussed several other examples of positive feedback loops in evolution. The analogy of Evolutionary arms races provide further examples of positive feedback in biological systems.

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

Immune system

A cytokine storm, or hypercytokinemia is a potentially fatal immune reaction consisting of a positive feedback loop between cytokines and immune cells, with highly elevated levels of various cytokines. In normal immune function, positive feedback loops can be utilized to enhance the action of B-lymphocytes. When a B-cell binds its antibodies to an antigen and becomes activated, it begins releasing antibodies and secreting a complement protein called C3. Both C3 and a B-cell's antibodies can bind to a pathogen, and when a B-cell has its antibodies bind to a pathogen with C3, it speeds up that B-cell's secretion of more antibodies and more C3, thus creating a positive feedback loop.

Psychology

In psychology, the body receives a stimulus from the environment or internally that causes the release of hormones. Release of hormones then may cause more of those hormones to be released, causing a positive feedback loop. This cycle is also found in certain behaviour. For example, "shame loops" occur in people who blush easily. When they realize that they are blushing, they become even more embarrassed, which leads to further blushing, and so on.

Winner (1996) described gifted children 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. Winner termed this positive feedback loop as a "rage to master."

Vandervert (2009) proposed that the child prodigy 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. Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for language evolution in working memory.

In substance dependence a human seeks the effects of a drug, and the drug supplies an effect. The human thereafter continues to seek the effects from the drug. In time the body acclimates to the dosage of the drug, and finds a new homeostasis. The human then must consume a larger quantity of the drug to feel the effects the subject wants, a drug overdose may occur when seeking this new threshold of drug effect. If an accidental overdose doesn't kill the human, eventually the human body can no longer repair itself from the damage (ex. Kidney failure and Liver failure) and death is the final result to this positive feedback.

Economics

Market dynamics

According to the theory of reflexivity advanced by George Soros, price changes are driven by a positive feedback process whereby investors' expectations are influenced by price movements so their behaviour acts to reinforce movement in that direction until it becomes unsustainable, whereupon the feedback drives prices in the opposite direction.

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: funds from new investors are used to pay out unusually high returns, which in turn attract more 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). Hyman Minsky proposed a theory that certain credit expansion practices could make a market economy into "a deviation amplifying system" that could suddenly collapse, sometimes called a "Minsky moment". 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. The 2010 Flash Crash incident was blamed on the practice of high-frequency trading (HFT), although whether HFT really increases systemic risk remains controversial.

Human population growth

Agriculture and human population can be considered to be in a positive feedback mode, 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. Technological innovation and human population can be similarly considered, and this has been offered as an explanation for the apparent hyperbolic growth of the human population in the past, instead of a simpler exponential growth. It is proposed that the growth rate is accelerating because of second-order positive feedback between population and technology. Technological growth increases the carrying capacity of land for people, which leads to more population, and so more potential inventors in further technological growth.

Prejudice, social institutions and poverty Gunnar Myrdal described a vicious circle of increasing inequalities, and poverty, which is known as "circular cumulative causation".

In meteorology

Drought intensifies through positive feedback. A lack of rain decreases soil moisture, which kills plants and/or causes them to release less water through transpiration. Both factors limit evapotranspiration, the process by which water vapor is added to the atmosphere from the surface, and add dry dust to the atmosphere, which absorbs water. Less water vapor means both low dew point temperatures and more efficient daytime heating, decreasing the chances of humidity in the atmosphere leading to cloud formation. Lastly, without clouds, there cannot be rain, and the loop is complete.

In climatology

The climate system is characterized by strong positive and negative feedback loops between processes that affect the state of the atmosphere, ocean, and land.
Climate "forcings" may push a climate system in the direction of warming or cooling, for example, increased atmospheric concentrations of greenhouse gases cause warming at the surface. Forcings are external to the climate system and feedbacks are internal processes of the system. Some feedback mechanisms act in relative isolation to the rest of the climate system while others are tightly coupled. Forcings, feedbacks and the dynamics of the climate system determine how much and how fast the climate changes. The main positive feedback in global warming is the tendency of warming to increase the amount of water vapour in the atmosphere, which in turn leads to further warming. The main negative feedback comes from the Stefan–Boltzmann law, the amount of heat radiated from the Earth into space is proportional to the fourth power of the temperature of Earth's surface and atmosphere.
Other examples of positive feedback subsystems in climatology include:
A warmer atmosphere will melt ice and this changes the albedo which further warms the atmosphere. This is called the ice-albedo positive feedback loop whereby melting snow exposes more dark ground (of lower albedo), which in turn absorbs heat and causes more snow to melt.
Methane hydrates can be unstable so that a warming ocean could release more methane, which is also a greenhouse gas.

The Intergovernmental Panel on Climate Change

IPCC's Fourth Assessment Report states that "Anthropogenic warming could lead to some effects that are abrupt or irreversible, depending upon the rate and magnitude of the climate change."

In sociology

A self-fulfilling prophecy is a social positive feedback loop between beliefs and behaviour: if enough people believe that something is true, their behaviour can make it true, and observations of their behaviour may in 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.

On the Internet

Internet recommendation systems are expected to increase the diversity of what we see and do online. They help us discover new content and websites among myriad choices. Some recommendation systems, however, unintentionally do the opposite. Because some recommendation systems (i.e. certain collaborative filters) recommend products based on past sales or ratings, they cannot usually recommend products with limited historical data. This can create positive feedback: a rich-get-richer effect for popular products. This bias toward popularity can prevent what are otherwise better recommendations for that user's preferences. A Wharton study details this phenomenon along with several ideas that may promote diversity.

Chemistry

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.

Similar terminology

1. Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop.
2. Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour (B.F. Skinner).
3. Praise of performance: a term often applied in the context of performance appraisal, although this usage is disputed.
4. Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage.