Positive feedback, sometimes referred to as "cumulative causation", refers to a situation where some effect causes more of itself. A system undergoing positive feedback is unstable, that is, it will tend to spiral out of control as the effect amplifies itself.
Technically, a system exhibiting positive
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
responds to perturbation in the same direction as the perturbation. That is, "A produces more of B which in turn produces more of A". In contrast, a system that responds to the perturbation in the opposite direction is said to exhibit
negative feedbackNegative feedback occurs when the output of a system acts to oppose changes to the input of the system; with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...
. These concepts were first recognized as broadly applicable by
Norbert WienerNorbert Wiener was an American pure and applied mathematician.A famous child prodigy, Wiener went on to become a pioneer in the study of stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is the founder of...
in his 1948 work on
cyberneticsCybernetics is the interdisciplinary study of the structure of regulatory systems. Cybernetics is closely related to control theory and systems theory...
.
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. A negative feedback loop tends to reduce or inhibit a process, while a positive feedback loop tends to expand or promote it.
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 a positive feedback is often amplifying and "explosive," i.e. a small perturbation results in big changes. Indeed, chemical- and nuclear
fissionFission is a splitting of something into two parts.Fission may refer to:*In physics, nuclear fission is a process where a large atomic nucleus is split into two smaller particles....
-based explosives offer an excellent physical demonstration of positive feedback. Bombarding a single atom of Uranium 235 with a neutron causes it to emit two neutrons, which can hit two more atoms, which in turn can hit a maximum of four atoms, etc. The number of atoms involved increases exponentially and very soon the entire mass of Uranium is involved.
Formally, a system in
equilibriumEquilibrium is the condition of a system in which competing influences are balanced and it may refer to:-Mathematics:* The stationary point of a dynamical system is often called an123 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 pointSet point or setpoint might mean one of:* Set point , a tennis term meaning one player is one point away from winning a set* Set point , a term referring to any one of a number of quantities Set point or setpoint might mean one of:* Set point (tennis), a tennis term meaning one player is one 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 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. A variety of negative feedback loops in the same system can modulate the effect. Embedded in a system of positive and negative feedback loops, positive feedback does not necessarily imply a runaway process. Combined with other processes, it may just have an amplifying effect.
In biology
One example of a biological positive feedback loop is the onset of
contractionsIn medicine , a contraction is a forceful and very painful motion of the uterus as part of the process of childbirth. Contractions, and labour in general, is one condition that releases the hormone oxytocin into the body. Contractions become longer as labour intensifies. At the start of labor,...
in
childbirthChildbirth is the culmination of a human pregnancy or gestation period with birth of one or more newborn infants from a woman's uterus...
. When a contraction occurs, the hormone
oxytocinOxytocin is a mammalian hormone that also acts as a neurotransmitter in the brain.It is best known for its roles in female reproduction: it is released in large amounts after distension of the cervix and vagina during labor, and after stimulation of the nipples, facilitating birth and...
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 clottingCoagulation is a complex process by which blood forms clots. It is an important part of hemostasis , wherein a damaged blood vessel wall is covered by a platelet and fibrin-containing clot to stop bleeding and begin repair of the damaged vessel...
. 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.
LactationLactation describes the secretion of milk from the mammary glands, the process of providing that milk to the young, and the period of time that a mother lactates to feed her young. The process occurs in all female mammals, and in humans it is commonly referred to as breastfeeding or nursing...
involves positive feedback so that the more the baby suckles, the more milk is produced.
EstrogenEstrogens are a group of steroid compounds, named for their importance in the estrous cycle, and functioning as the primary female sex hormone, their name comes from estrus/oistros + gen/gonos = to generate.Estrogens are used as part of some oral contraceptives, in estrogen replacement...
that functions during the follicular phase of menstruation is also an example of positive feedback.
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 potentialAn action potential is a transient alteration of the transmembrane voltage across an excitable membrane generated by the activity of voltage-gated ion channels embedded in the membrane. Action potentials play multiple roles in several types of excitable cells such as neurons, myocytes, and...
.
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.
The above and other other examples of positive feedback systems in physiology are fairly well described in
Arthur GuytonArthur Clifton Guyton was an American physiologist. He was born in Oxford, Mississippi, to Dr. Billy S. Guyton, a highly respected eye, ear, nose, and throat specialist, who later became Dean of the University of Mississippi Medical School, and Kate Smallwood Guyton, a mathematics and physics...
's 'Textbook of Medical Physiology'.
Evolutionary arms raceIn evolutionary biology, an evolutionary arms race is an evolutionary struggle between competing sets of co-evolving genes that develop adaptations and counter-adaptations against each other, resembling an arms race, which are also examples of positive feedback...
s provide further examples of positive feedback in biological systems.
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
feed-forwardFeed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in the control system's external environment, often a command signal from an external operator, to a load elsewhere in its external environment...
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
feed-forwardFeed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in the control system's external environment, often a command signal from an external operator, to a load elsewhere in its external environment...
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 (
Ai) increases.
If the circuit elements are practically linear, the 'internal gain',
Ai , of the feedback loop is given by
Ai = (output voltage/input voltage) =
A/ (1 −
Aβ). Here
A is the gain of the
feed-forwardFeed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in the control system's external environment, often a command signal from an external operator, to a load elsewhere in its external environment...
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
feed-forwardFeed-forward is a term describing an element or pathway within a control system which passes a controlling signal from a source in the control system's external environment, often a command signal from an external operator, to a load elsewhere in its external environment...
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
In electrical engineering, specifically signal processing and control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. BIBO stands for Bounded-Input Bounded-Output...
is difficult or impossible to guarantee
Positive feedback is used extensively in oscillators and in regenerative
radio receiversThis article is about a radio receiver, for other uses see Radio .A radio receiver is an electronic circuit that receives its input from an antenna, uses electronic filters to separate a wanted radio signal from all other signals picked up by this antenna, amplifies it to a level suitable for...
and Q multipliers.
The
schmitt triggerIn electronics, a Schmitt trigger is a comparator circuit that incorporates positive feedback.When the input is higher than a certain chosen threshold, the output is high; when the input is below another chosen threshold, the output is low; when the input is between the two, the output retains its...
circuit uses positive feedback to generate
hysteresisA system with hysteresis has memory. Such a system is said to exhibit path-dependence, or "rate-independent memory". .In a deterministic system with no dynamics or hysteresis, it is possible to predict the system's output at an instant in time, given only its input at that instant in time...
and thus provide
noiseIn common use, the word noise means unwanted sound or noise pollution. In both analog and digital electronics, noise or signal noise is an unwanted random addition to a wanted signal; it is called noise as a generalisation of the audible noise heard when listening to a weak radio transmission...
immunity on
digitalA digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
input.
Audio feedbackAudio feedback is a special kind of feedback which occurs when a sound loop exists between an audio input and an audio output...
or acoustic feedback is a common example of positive feedback. It is the familiar squeal that results when sound from
loudspeakerA loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker pulses in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water.Loudspeakers are the most variable elements in a...
s enters a closely-placed
microphoneA microphone, colloquially called a mic or mike , is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1876, Emile Berliner invented the first microphone used as a telephone voice transmitter...
and gets amplified, and as a result the
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
gets louder and louder. To avoid this condition, the
microphoneA microphone, colloquially called a mic or mike , is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1876, Emile Berliner invented the first microphone used as a telephone voice transmitter...
must be prevented from "hearing" its own
loudspeakerA loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker pulses in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water.Loudspeakers are the most variable elements in a...
.
In economics
In the World System development
The
exponential growthExponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
of the
world populationThe term world population commonly refers to the total number of living humans on Earth at a given time. As of , the Earth's population is estimated by the United States Census Bureau to be billion. The world population has been growing continuously since the end of the Black Death around 1400...
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 capacityThe carrying capacity of a biological species in an environment is the population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...
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 KorotayevAndrey Korotayev is an anthropologist, economic historian, and sociologist, with major contributions to World-systems theory and mathematical modeling of social and economic macrodynamics.- Education and Carrier :...
et al.).
Systemic risk
Systemic riskIn finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system. It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by...
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 schemeA Ponzi scheme is a fraudulent investment operation that pays returns to separate investors from their own money or money paid by subsequent investors, rather than from any actual profit earned. The Ponzi scheme usually entices new investors by offering return other investments cannot guarantee,...
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 ArthurWilliam Brian Arthur is an economist credited with influencing and describing the modern theory of increasing returns. He has lived and worked in Northern California for many years. He is a sought-after speaker on economics and complexity theory in technology and financial markets, and other...
has also studied and written on positive feedback in the economy (e.g. W. Brian Arthur, 1990)
Simple systems that clearly separate the inputs from the outputs are not prone to
systemic riskIn finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system. It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by...
. 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, 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 riskIn finance, systemic risk is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system. It can be defined as "financial system instability, potentially catastrophic, caused or exacerbated by...
.
In climate
Examples in climate include:
- A warmer atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, by the gravity of the body, and are retained for a longer duration if gravity is high and the atmosphere's temperature is low...
will, due to increased evaporation and decreased condensation, contain more water vapour which is a greenhouse gasGreenhouse gases are gases in an atmosphere that absorb and emit radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The main greenhouse gases in the Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone...
so it will warm the atmosphere further.
- A warmer atmosphere will melt ice and this changes the albedo
The albedo of an object is the extent to which it diffusely reflects light from light sources such as the Sun. It is therefore a more specific form of the term reflectivity. Albedo is defined as the ratio of diffusely reflected to incident electromagnetic radiation. It is a unitless measure...
which further warms the atmosphere.
- A colder climate will cause ice caps and glaciers to grow changing the albedo
The albedo of an object is the extent to which it diffusely reflects light from light sources such as the Sun. It is therefore a more specific form of the term reflectivity. Albedo is defined as the ratio of diffusely reflected to incident electromagnetic radiation. It is a unitless measure...
which further cools the atmosphere.
- Methane hydrates can be unstable such that a warming ocean could release methane which is a greenhouse gas.
On earth the
gainGain is a measure of a system's response to feedback. If the gain in a positive feedback loop is less than 1, the feedback is not of itself sufficient to make the system become unstable. For example, water evaporating from the World's oceans causes a positive feedback, as it is a greenhouse gas...
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 ageThe general term "ice age" or, more precisely, "glacial age" denotes a geological period of long-term reduction in the temperature of the Earth's surface and atmosphere, resulting in an expansion of continental ice sheets, polar ice sheets and alpine glaciers. Within a long-term ice age, individual...
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 prophecyA self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true, by the very terms of the prophecy itself, due to positive feedback between belief and behavior. Although examples of such prophecies can be found in literature as far back as ancient Greece and...
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 runA bank run occurs when a large number of bank customers withdraw their deposits because they believe the bank is, or might become, insolvent...
.
Another sociological example of positive feedback is the
network effectIn economics and business, a network effect is the effect that one user of a good or service has on the value of that product to other people....
, 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 Jaehwan scheme. In this case the population size is the limiting factor.
See also
- Chain reaction
A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events...
- Donella Meadows' twelve leverage points to intervene in a system
- Greenhouse effect
The greenhouse effect is the heating of the surface of a planet or moon due to the presence of an atmosphere containing gases that absorb and emit infrared radiation. Thus, greenhouse gases trap heat within the surface-troposphere system...
- Hyperbolic growth
When a quantity grows towards a singularity under a finite variation it is said to undergo hyperbolic growth.More precisely, the reciprocal function has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as is infinity: any similar graph is said to exhibit hyperbolic...
- Negative feedback
Negative feedback occurs when the output of a system acts to oppose changes to the input of the system; with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...
- Reflexivity (social theory)
In sociology, reflexivity is an act of self-reference where examination or action 'bends back on', refers to, and affects the entity instigating the action or examination. In brief, reflexivity refers to circular relationships between cause and effect...
- Strategic complementarity
- Stability criterion
- System dynamics
System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. What makes using system dynamics different from other approaches to studying complex systems is the use...
- Thermal runaway
Thermal runaway refers to a situation where an increase in temperature changes the conditions in a way that causes a further increase in temperature leading to a destructive result. It is a kind of positive feedback.-Chemical engineering:...
Examples
- Bus bunching
Bus bunching is either of two things: a bus route having highly irregular service intervals, and a classical theory for a causal model for irregular intervals, on the premise that a late bus tends to get later and later as it completes its run, while the bus following it tends to get earlier and...
- Cytokine storm
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.-Symptoms:...
- Matthew effect
The Matthew effect in sociology is the phenomenon that "the rich get richer and the poor get poorer". Those who possess power and economic or social capital can leverage those resources to gain more power or capital. The Matthew effect results in a power law distribution of resources. The term...
- Autocatalysis
A single chemical reaction is said to have undergone autocatalysis, or be autocatalytic, if the reaction product is itself the catalyst for that reaction....
- Meander
A meander in general is a bend in a sinuous watercourse. A meander is formed when the moving water in a river erodes the outer banks and widens its valley. A stream of any volume may assume a meandering course, alternatively eroding sediments from the outside of a bend and depositing them on the...
- Runaway greenhouse effect
A runaway greenhouse effect occurs when, on a planet with substantial reserves of greenhouse gases in liquid or solid form, some forcing occurs to begin to gasify them, leading via positive feedback to complete gasification of these reserves....
Further reading
- Norbert Wiener
Norbert Wiener was an American pure and applied mathematician.A famous child prodigy, Wiener went on to become a pioneer in the study of stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is the founder of...
(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
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology in Cambridge, Massachusetts .-History:...
. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.