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353:, this makes the populations of predators of 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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criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude. This can produce a steady and sustained oscillation. In some cases, self-oscillation can be
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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
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Many early radio systems tuned their transmitter circuit, so the system automatically created radio waves of the desired frequency. This design has given way to designs that use a separate oscillator to provide a signal that is then amplified to the desired power.
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is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from
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The same phenomenon is sometimes labelled as "maintained", "sustained", "self-exciting", "self-induced", "spontaneous", or "autonomous" oscillation. Unwanted self-oscillations are known in the mechanical engineering literature as
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There are many examples of self-exciting oscillation 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.
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that acts on the oscillator. If the power is modulated in phase with the oscillator's velocity, a negative damping is established and the oscillation grows until limited by nonlinearities.
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considered various instances of mechanical and acoustic self-oscillations (which he called "maintained vibration") and offered a simple mathematical model for them.
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that he showed correspond to electrical oscillations with frequencies of hundreds of millions of cycles per second. Hertz's work led to the development of
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between the oscillation and the modulation of the external source of power. The amplitude and waveform of steady self-oscillations are determined by the
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Alicki, Robert; Horodecki, Michal; Jenkins, Alejandro; Lobejko, Marcin; Suarez, Gerardo (2023). "The
Josephson junction as a quantum engine".
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Simple mathematical models of self-oscillators involve negative linear damping and positive non-linear damping terms, leading to a
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is connected to a capacitor and the shaft turns above synchronous speed, it operates as a self-excited induction generator.
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can cause an uncomfortable wobbling effect, which in extreme cases can derail trains and cause cars to lose grip.
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term, which causes small perturbations to grow exponentially in amplitude. This negative damping is due to a
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produce the human voice. Another instance of self-oscillation, associated with the unstable operation of
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were guilty of self-exciting oscillation because they responded too quickly. The problem was overcome by
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The term "self-oscillation" (also translated as "auto-oscillation") was coined by the Soviet physicist
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Schematic representation of a self-oscillation as a positive feedback loop. The oscillator
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Self-oscillation is manifested as a linear instability of a dynamical system's static
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is one such model that has been used extensively in the mathematical literature.
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Self-oscillations are important in physics, engineering, biology, and economics.
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Interest in the subject of self-oscillation was also stimulated by the work of
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The study of self-oscillators dates back to the early 1830s, with the work of
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For example, a reduction in population of an herbivore species because of
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Steering of vehicles when course corrections are delayed
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291:Self-exciting oscillation occurred in early
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207:system, which makes the change in variable
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466:Maxwell, J. Clerk (1867). "On Governors".
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313:SEIG (self-excited induction generator)
203:seen as resulting from a time lag in a
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69:nonlinear characteristics of the system
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186:Oscillation (differential equation)
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98:, was studied mathematically by
575:Ordinary differential equations
221:evaluated at an earlier time.
90:on the mechanism by which the
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445:10.1016/j.physrep.2012.10.007
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245:Railway and automotive wheels
413:(2013). "Self-oscillation".
339:Population cycles in biology
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271:Central heating thermostats
133:in the early 20th century.
24:produces a feedback signal
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325:Self-exciting transmitters
214:dependent on the variable
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517:10.1088/1367-2630/ad06d8
334:Examples in other fields
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345:Lotka–Volterra equation
287:Automatic transmissions
240:Examples in engineering
164:in the 20th century.
495:New Journal of Physics
373:Van der Pol oscillator
293:automatic transmission
275:Early central heating
234:van der Pol oscillator
228:and the appearance of
174:parasitic oscillations
162:Philippe Le Corbeiller
78:History of the subject
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565:Mechanical vibrations
343:Further information:
154:Balthasar van der Pol
119:spark-gap transmitter
106:, published in 1896,
96:centrifugal governors
50:parametric resonators
28:. The controller at
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158:Alfred-Marie Liénard
142:structural stability
437:2013PhR...525..167J
250:Hunting oscillation
127:wireless telegraphy
104:The Theory of Sound
100:James Clerk Maxwell
88:George Biddell Airy
570:Physical phenomena
411:Jenkins, Alejandro
378:Hidden oscillation
180:Mathematical basis
138:Aleksandr Andronov
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560:Nonlinear systems
555:Dynamical systems
300:into the system.
146:dynamical systems
65:positive feedback
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121:to generate
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540:Oscillators
474:: 270–283.
368:Limit cycle
277:thermostats
205:closed loop
192:equilibrium
123:radio waves
92:vocal cords
545:Amplifiers
534:Categories
508:2302.04762
501:: 113013.
384:References
298:hysteresis
281:hysteresis
453:227438422
428:1109.6640
351:predation
580:Feedback
357:See also
433:Bibcode
254:railway
232:. The
200:Nyquist
170:hunting
61:damping
480:112510
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317:If an
261:shimmy
257:wheels
160:, and
46:forced
503:arXiv
476:JSTOR
449:S2CID
423:arXiv
265:tires
259:and
198:and
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216:x
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