Hunting (engineering)
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Hunting is a self-exciting oscillation of a system, and is common in systems which incorporate feedback. It is an important phenomenon in many fields, including engineering, economics and biology.
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[edit] Mathematical basis of hunting
Self-exciting oscillations are a logical consequence of systems which are described by a closed loop of time-lagged differential equations, i.e. where a change in variable N is driven by a change in variable N+1 but only after a time delay, a change in variable N+1 is driven by a change in variable N+2 but only after a time delay, .... a change in variable N is driven by a change in variable N+x but only after a time delay.
[edit] Examples in Engineering
[edit] Railway and automotive wheels
Hunting in railway wheels and shimmy in automotive tires can cause an uncomfortable wobbling effect, which in extreme cases can derail trains and cause cars to lose grip.
For a mathematical analysis of the phenomenon in the context of railway vehicle dynamics, see Hunting oscillation.
[edit] Central heating thermostats
Early central heating thermostats were guilty of hunting because they responded too quickly. The problem was overcome by hysteresis, i.e., making them switch state only when the temperature varied from the target by a specified minimum amount.
[edit] Automatic transmissions
Hunting occurred in early automatic transmission designs when the vehicle was traveling at a speed which was between the ideal speeds of 2 gears. In these situations the transmission system would switch almost continuously between the 2 gears, which was both annoying and hard on the transmission. Such behavior is now inhibited by introducing hysteresis into the system.
[edit] Steering of vehicles when course corrections are delayed
There are many examples of hunting caused by delayed course corrections, ranging from light aircraft in a strong wind to erratic steering of road vehicles by a driver who is inexperienced or drunk.
[edit] Examples in other fields
[edit] Boom-bust cycles in economics
No doubt in practice these are partly due to herd psychology, but closed loops of time-lagged differential equations are a sufficient explanation. In economics the time delay is caused by the need for individuals and organizations to gather information and make decisions. The classic example is the stock market: prices start rising, after a while investors notice this and increase their buying, this forces prices up, etc. - until something (e.g. a scandal or an economic crisis) stops prices from rising, after a while investors decide to sell, etc.
[edit] Population cycles in biology
For example the population of a herbivore species because of e.g. illness, this makes the populations of predators on that species decline, the reduced level of predation allows the herbivore population to increase, this allows the predator population to increase, etc. Closed loops of time-lagged differential equations are a sufficient explanation for such cycles - in this case the delays are caused mainly by the breeding cycles of the species involved.
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