Positive feedback

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Overview

Positive feedback is the feedback loop system in which the system responds to perturbation in the same direction as the perturbation (It is sometimes referred to as cumulative causation). 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.*

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 one with negative feedback is said 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 setpoint, 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, the process accelerates until the fissile material is spent or dispersed by the resulting explosion.

Both positive and negative feedback are closed systems, because the system is closed by a feedback loop, i.e. the response of the system depends on the feedback signal to complete its function; without such a loop, it would become an open system. In contrast, a feed-forward system is an "open system" since it does not have any feedback loop, and does not rely on feedback signal to function.

Examples of positive and negative feedback, open and closed systems can be found in ecological, biological, social systems and in engineering control systems such as servo control systems.

Explanation

The effect of a positive feedback loop is not necessarily "positive" in the sense of being desirable. The name refers to the nature of change rather than the desirability of the outcome. The negative feedback loop tends to slow down a process, while the positive feedback loop tends to speed it up.

When a change of 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 of course always true for a negative feedback but also for lower positive feedbacks. 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, a positive feedback does not necessarily imply a runaway process. Combined with other processes, it may just have an amplifying effect. An example of this is the role of water vapour in amplifying global warming; higher global temperatures lead to increased water vapour in the atmosphere, which pushes up temperatures further, and so on, but the overall effect is that of a convergent series, amplifying the original temperature rise by a relatively constant factor. The limiting control is that water vapour does not depend solely upon temperature. Water cycles in and out of the atmosphere for a variety of reasons.

One common example of positive feedback is the network effect, where more people are encouraged to join a network the larger that 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.

In Electronics

Feedback is a process of sampling a part of the output signal and applying it back to the input. This technique is useful to change the parameters of an amplifier like voltage gain, input and output impedance, stability and bandwidth.

Feedback is said to be positive if any increase in the output signal results in a feedback signal which on being mixed with the input signal caused 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 final gain of the amplifier(A_f) increases.

Final gain A_f=(output voltage/input voltage)=A/(1-Aβ). Here A is the gain of the amplifier without feedback, and β is the feedback factor

Disadvantages

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

Applications

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 is a common example of positive feedback. It is the familiar squeal that results when sound from loudspeakers enters a poorly placed microphone and gets amplified, and as a result the sound gets louder and louder.

In the world system development

The hyperbolic growth of the world population observed till 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.).

Population and Agriculture

In Feed or Feedback A. Duncan Brown argues that agriculture and human population are in a positive feedback mode, which means that one drives the other with increasing intensity. He ventures the case that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and turning to monocultures which are more susceptible to collapse.

Echo Chamber Effect

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 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 which activate platelets in the blood. An activated platelet releases chemicals which activate more platelets, causing a rapid cascade and the formation of a blood clot.

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

References

• 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.

See also

• Donella Meadows' twelve leverage points to intervene in a system
• Reflexivity (social theory)
• Strategic complementarity
• Stability criterion
• Virtuous circle and vicious circle
• Matthew effect
• Bus bunching
• Hyperbolic growth
• W. Brian Arthur, economist noted for his works studying postitive feedback