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