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Repetitive variation of some measure about a central value
different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations are often used in physics to approximate
Oscillation
Academic journal
Nonlinear Oscillations is a quarterly peer-reviewed mathematical journal that was established in 1998. It is published by Springer Science+Business Media
Nonlinear_Oscillations
System where changes of output are not proportional to changes of input
orbits to which destabilized fixed points are attracted. Self-oscillations – feedback oscillations taking place in open dissipative physical systems. Algebraic
Nonlinear_system
Oscillator that produces a nonsinusoidal repetitive waveform
Balthasar van der Pol first distinguished relaxation oscillations from harmonic oscillations, originated the term "relaxation oscillator", and derived
Relaxation_oscillator
Physical phenomenon
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. In nonlinear resonance the system behaviour – resonance frequencies
Nonlinear_resonance
Physical phenomenon
oscillation. Unwanted self-oscillations are known in the mechanical engineering literature as hunting, and in electronics as parasitic oscillations.
Self-oscillation
Field of mathematics and science based on non-linear systems and initial conditions
ISBN 978-0-521-47685-0. Guckenheimer, John; Holmes, Philip (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag
Chaos_theory
Phenomenon in which a neutrino changes lepton flavor as it travels
produced in nuclear reactors. No oscillations were found until a detector was installed at a distance 1–2 km. Such oscillations give the value of the parameter
Neutrino_oscillation
Atmospheric electrical phenomenon
spherically symmetric nonlinear oscillations of charged particles in plasma – the analogue of a spatial Langmuir soliton. These oscillations were described in
Ball_lightning
Brainwaves, repetitive patterns of neural activity in the central nervous system
interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action
Neural_oscillation
Russian-American engineer and scientist (1885–1970)
relaxation oscillations. J.W. Edwards. ISBN 978-93-336-9885-6. {{cite book}}: ISBN / Date incompatibility (help) Minorsky, N. (1958). Dynamics and Nonlinear Mechanics:
Nicolas_Minorsky
Deviation of a physical system from being a harmonic oscillator
use nonlinear equations of motion to describe their behavior. Anharmonicity plays a role in lattice and molecular vibrations, in quantum oscillations, and
Anharmonicity
Branch of physics
Nonlinear optics (NLO) is a branch of optics that studies the case when optical properties of matter depend on the intensity of the input light. Nonlinear
Nonlinear_optics
Type of electronic circuit
in the form of electronic oscillations if excited, but because it has electrical resistance and other losses the oscillations are damped and decay to zero
Electronic_oscillator
Topics referred to by the same term
behavior in solids of large amplitude oscillations of phonons, elementary vibrations of the crystal lattice Nonlinear resonance, accumulation of vibrations
Nonlinearity_(disambiguation)
Apparent force in a rotating reference frame
Bhatia, V.B. (1997). Classical Mechanics: With introduction to Nonlinear Oscillations and Chaos. Narosa Publishing House. p. 201. ISBN 978-81-7319-105-3
Coriolis_force
Formulas to determine the energy balance of a nonlinear wave
group on nonlinear oscillations. This group was later joined by Peterson, Manley, and Rowe. Geoffrey New (2011). Introduction to Nonlinear Optics. Cambridge
Manley–Rowe_relations
Ferroresonance, or nonlinear resonance, is a rare type of resonance in electric circuits which occurs when a circuit containing a nonlinear inductance is fed
Ferroresonance in electricity networks
Ferroresonance_in_electricity_networks
Control theory for nonlinear or time-variant systems
Nonlinear control theory is an area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary
Nonlinear_control
Differential equation exhibiting high rate of dissipation
accounting for a full period. The problem originates in the study of nonlinear oscillations in electric circuits. For large values of κ {\displaystyle \kappa
Stiff_equation
American physicist (born 1943)
Physicists. He has made significant contributions to the theory of nonlinear oscillations and numerical analysis. Ronald Elbert Mickens was born February
Ronald_E._Mickens
(1996). Oscillations in Planar Dynamic Systems. World Scientific. ISBN 981-02-2292-0. Mickens, Ronald E. (2010). Truly Nonlinear Oscillations: Harmonic
List of Vanderbilt University people
List_of_Vanderbilt_University_people
Physics award
University "groundbreaking work on non-equilibrium systems, especially nonlinear oscillations, synchronization, and weak turbulence. Professor Kuramoto’s work
Boltzmann_Medal
American electronics researcher (1888–1970)
research group at Bell Laboratories starting in 1929 to investigate nonlinear oscillations and what later became known as parametric amplifiers. This research
Ralph_Hartley
Graduate-level textbooks in mathematics
Chandrasekharan 1950 219 978-0691095783 20 Contributions to the Theory of Nonlinear Oscillations, Volume I Edited by Solomon Lefschetz 1950-04-21 360 978-0691079318
Annals_of_Mathematics_Studies
Neuron communication by electric impulses
Excitability and Oscillations, pp. 135–169. Biswas A, Manivannan M, Srinivasan MA (2015). "Vibrotactile sensitivity threshold: nonlinear stochastic mechanotransduction
Action_potential
Palestinian-Jordanian engineer specialising in non-linear dynamics
perturbation techniques, nonlinear oscillations, aerodynamics, flight mechanics, acoustics, ship motions, hydrodynamic stability, nonlinear waves, structural
Ali_H._Nayfeh
Awarded every year by the American Mathematical Society
ISBN 978-1-4704-6853-8. Guckenheimer, John; Holmes, Philip (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical
Leroy_P._Steele_Prize
Disproved conjecture
instability in nonlinear automatic control systems". Transactions of ASME. 79 (3): 553–566. Kuznetsov N.V. (2020). "Theory of hidden oscillations and stability
Kalman's_conjecture
Group of carnivorous mammals
predators of rabbits and hens. Population oscillations of these two species were the first nonlinear oscillation studied and led to the derivation of the
Fox
York Journal of Mathematics Nieuw Archief voor Wiskunde Nonlinear Oscillations Nonlinearity (journal) Notices of the American Mathematical Society Nouvelles
List_of_mathematics_journals
Behavior in a nonlinear system
where systems with self-sustained oscillations are modelled. Some examples include: Aerodynamic limit-cycle oscillations The Hodgkin–Huxley model for action
Limit_cycle
Concept in dynamical systems
fast oscillation versus a slow drift. It suggests that we perform an averaging over a given amount of time in order to iron out the fast oscillations and
Method_of_averaging
Mathematical concept
ISBN 978-0-387-35794-2. Guckenheimer, John; Holmes, Philip (1997), Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical
Center_manifold
Oscillating dynamical system with nonlinear damping
working at Philips. Van der Pol found stable oscillations, which he subsequently called relaxation-oscillations and are now known as a type of limit cycle
Van_der_Pol_oscillator
made to emit pulses of light by driving the bubble into highly nonlinear oscillations. This is done by the increasing pressure of the acoustic wave to
Mechanism_of_sonoluminescence
Fluctuations in stellar radius
S2CID 189850134. Guckenheimer, John; Holmes, Philip; Slemrod, M. (1984). "Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields". Journal of
Stellar_pulsation
Soviet mathematician and theoretical physicist (1909–1992)
the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kyiv school of nonlinear oscillation research", where
Nikolay_Bogolyubov
Professor
Tokyo, known for his contributions to nonlinear dynamics, mathematical modeling of neural systems, nonlinear oscillation, and engineering. The FitzHugh–Nagumo
Jinichi_Nagumo
Mechanism using friction to resist rotation of a circular plate
of passing through critical speed", In EuroMech – 2nd European Nonlinear Oscillations Conference, Prague, no. 2, pp. 75–78. Jacobsson, H. (1997), "Wheel
Disc_brake
theory, a bounded oscillation that is born without loss of stability of stationary set is called a hidden oscillation. In nonlinear control theory, the
Hidden_attractor
Strogatz, Steven. "Nonlinear Dynamics and Chaos". Westview Press, 2001. p. 52. Guckenheimer, John; Holmes, Philip (1983), Nonlinear Oscillations, Dynamical Systems
Normal form (dynamical systems)
Normal_form_(dynamical_systems)
Vibration that travels via pressure waves in matter
an extremely small effective gravitational mass. This mass arises from nonlinear corrections to the stress–energy of the wave, and implies that sound waves
Sound
Physical characteristic of oscillating systems
The ratio of the amplitude of the output's steady-state oscillations to the input's oscillations is called the gain, and the gain can be a function of the
Resonance
Condition determining when a linear electronic circuit will oscillate
determining the oscillation frequencies of the feedback loop, involved an equality sign: |βA| = 1. At the time conditionally-stable nonlinear systems were
Barkhausen stability criterion
Barkhausen_stability_criterion
Path between equilibrium points in a phase space
Homoclinic orbit Traveling wave John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, (Applied
Heteroclinic_orbit
American mathematician
Berkeley, where his Ph.D. thesis advisor was Stephen Smale. His book Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields (with Philip
John_Guckenheimer
Wave that remains in a constant position
The peak amplitude of the wave oscillations at any point in space is constant with respect to time, and the oscillations at different points throughout
Standing_wave
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world
List of nonlinear ordinary differential equations
List_of_nonlinear_ordinary_differential_equations
Closed loop through a phase space
Amer. Math. Soc.73, 747–817. John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical
Homoclinic_orbit
Type of nonlinear wave in physics
In physics, a breather is a nonlinear wave in which energy concentrates in a localized and oscillatory fashion. This contradicts with the expectations
Breather
Dependence of the state of a system on its history
systems with hysteresis". Proceedings of the Fourth Conference on Nonlinear Oscillation. Prague, Czechoslovakia. p. 315. Bouc, R. (1971). "Modèle mathématique
Hysteresis
Neural activity synching to external stimuli
cooperate, displaying oscillations in four frequency orders, from the infra-low (<0.01 Hz) to ultra-fast (200 Hz) oscillations: delta (0.5-4 Hz), theta
Brainwave_entrainment
Electronic resistor
exhibits chaotic oscillations and is widely used as an example for a chaotic system. It is implemented as a voltage-controlled, nonlinear negative resistor
Chua's_diode
Parametric oscillator that oscillates at optical frequencies
i {\displaystyle \omega _{s},\omega _{i}} ) by means of second-order nonlinear optical interaction. The sum of the output waves' frequencies is equal
Optical_parametric_oscillator
Quasiparticle of charge oscillations in condensed matter
plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the
Plasmon
French radio pioneer and army general
Encyclopaedia Britannica Ginoux, Jean-Marc (2017). History of Nonlinear Oscillations Theory in France (1880–1940). Springer International Publishing
Gustave-Auguste_Ferrié
Ukrainian mathematician
known for his contributions to the fields of dynamical systems and nonlinear oscillations. He was born in Poltava Governorate and died in Kyiv. He received
Yurii_Mitropolskyi
Number of occurrences or cycles per unit time
(SI) is the hertz, having the symbol Hz. For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term frequency
Frequency
Indian mathematician
Series in Applicable Analysis, World Scientific, Singapore Editor, Nonlinear Oscillations, The Publication of the Institute of Mathematics, National Academy
Ravi_Agarwal
Type of motion that is approximately periodic
ISBN 978-1-009-15114-6. Ginoux, Jean-Marc (18 April 2017). History of Nonlinear Oscillations Theory in France (1880-1940). Springer. pp. 311–312. ISBN 978-3-319-55239-2
Quasiperiodic_motion
la théorie des oscillations non linéaires [Influence of Henri Poincaré on the modern development of the theory of nonlinear oscillations]. Le livre du
List of works by Nicolas Minorsky
List_of_works_by_Nicolas_Minorsky
Branch of physics and acoustics
Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using
Nonlinear_acoustics
Fundamental model of low-dimensional nonlinear physics
Frenkel–Kontorova (FK) model is a fundamental model of low-dimensional nonlinear physics. The generalized FK model describes a chain of classical particles
Frenkel–Kontorova_model
Range 300-3000 GHz of the electromagnetic spectrum
Vasanelli, Angela; Sirtori, Carlo; Todorov, Yanko (February 2023). "Nonlinear Oscillation States of Optomechanical Resonator for Reconfigurable Light-Compatible
Terahertz_radiation
Branch of engineering and mathematics
decrease from their initial value and do not show permanent oscillations. Permanent oscillations occur when a pole has a real part exactly equal to zero (in
Control_theory
French-American mathematician and electrical engineer
production des oscillations". Onde Électrique. 12: 116–148. Le Corbeiller, P. (1933). "Les systèmes autoentretenus et les oscillations de relaxation"
Philippe_Le_Corbeiller
Russian physicist
Chaotic Oscillations (1987, with Yuri Neimark) Nonlinear Oscillations and Waves in Dynamical Systems (1996) Regular and Chaotic Oscillations (2001) "Natural
Polina_Landa
Exactly solvable model of coupled oscillators
is coupled equally to all other oscillators. Surprisingly, this fully nonlinear model can be solved exactly in the limit of infinite oscillators, N →
Kuramoto_model
Self-oscillation about an equilibrium that is usually unwanted
vehicle is being driven on-rail. Two common "hunting" oscillations in aviation are the phugoid oscillation, in which the plane's natural trim mechanism "hunts"
Hunting_oscillation
American mathematician
McKenna, P. J. (1989). "Existence and stability of large scale nonlinear oscillations in suspension bridges". Zeitschrift für Angewandte Mathematik und
Joseph_Glover
Kuznetsov N.V.; Leonov G.A. (2011). "Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits"
Aizerman's_conjecture
Unexpectedly large transient ocean surface wave
waves. Among other causes, studies of nonlinear waves such as the Peregrine soliton, and waves modeled by the nonlinear Schrödinger equation (NLS), suggest
Rogue_wave
Indian educator and researcher
Hatwal, H.; Mallik, A. K.; Ghosh, Amitabha (September 1983). "Forced Nonlinear Oscillations of an Autoparametric System—Part 1: Periodic Responses". Journal
Amitabha Ghosh (academic, born 1941)
Amitabha_Ghosh_(academic,_born_1941)
Type of feedforward neural network
feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish
Multilayer_perceptron
French physicist and engineer (1892–1965)
retrieved 2017-10-22 Ginoux, Jean-Marc (2017-05-26), History of Nonlinear Oscillations Theory in France (1880–1940), Springer International Publishing
Lucien_Lévy
Fundamental interaction between charged particles
proportional change of the fields. Nonlinear dynamics can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This is studied
Electromagnetism
Ukrainian mathematician (1938–2020)
differential equations, nonlinear mechanics, and the theory of nonlinear oscillations. His results in the theory of multifrequency oscillations, perturbation theory
Anatoly_Samoilenko
Signal processing technique
A heterodyne is the result of mixing two signals in a nonlinear device to produce new frequency components, notably sum and difference frequencies of
Heterodyne
of congress catalog card number: 69-13487, page 1. Minorsky, N. Nonlinear Oscillations. Krieger Publishing (June 1974). ISBN 0882751867. E.I. Butikov (2005)
Mechanical_amplifier
Lowest possible energy of a quantum system or field
electromagnetic oscillations also can never cease completely. Thus the quantum nature of the electromagnetic field has as its consequence zero point oscillations of
Zero-point_energy
Electronic circuit that behaves chaotically
before it can display chaotic behaviour. It must contain: one or more nonlinear elements, one or more locally active resistors, three or more energy-storage
Chua's_circuit
Russian-American probability theorist
Freidlin, Mark I. (1998). "Random and deterministic perturbations of nonlinear oscillations". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III.
Mark_Freidlin
Limiting set in dynamical systems
nonlinear can give rise to a richer variety of behavior than can linear systems. One example is Newton's method of iterating to a root of a nonlinear
Attractor
Slovenian-British biophysicist
research concerns biological oscillations, particularly in the blood circulatory system, and their analysis using wavelets, nonlinear systems, and the Kuramoto
Aneta_Stefanovska
Soviet Russian physicist
theory of oscillations" was published in 1929 in the Proceedings of the Paris Academy of Sciences. It laid the foundation for the theory of nonlinear oscillations
Aleksandr_Andronov
459–478. ISBN 978-0-415-32868-5. Guckenheimer J, Holmes P (1986). Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (2nd printing
Quantitative models of the action potential
Quantitative_models_of_the_action_potential
Harmonic oscillator whose parameters oscillate in time
parameter. Parametric oscillations were first noticed in mechanics. Michael Faraday (1831) was the first to notice oscillations of one frequency being
Parametric_oscillator
Mat. Obs. 12: 3–52. Guckenheimer, John; Holmes, Philip (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer
Melnikov_distance
Property that an increasing voltage results in a decreasing current
i_{0}} to start spontaneous oscillations, which grow exponentially. However, the oscillations cannot grow forever; the nonlinearity of the diode eventually
Negative_resistance
Indian theoretical physicist
lectures titled Topics in Nonlinear Dynamics. A fifth series entitled Basic Concepts of Elementary Physics : Mechanics, Heat, Oscillations, Waves and Thermal
V._Balakrishnan_(physicist)
Russian scientist
Leningrad, USSR) is a specialist in nonlinear dynamics and control theory, and the founder of the theory of hidden oscillations. He graduated from the St. Petersburg
Nikolay_V._Kuznetsov
for the series of works “New analytical methods in the theory of nonlinear oscillations, the theory of random matrices and in characterization problems”
Gennadiy_Feldman
another can generate periodic oscillations. The describing function method attempts to predict characteristics of those oscillations (e.g., their fundamental
Describing_function
Idea that small causes can have large effects
initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely
Butterfly_effect
Turrittin (1952). S. Lefschetz (ed.). Contributions to the Theory of Nonlinear Oscillations (AM-29). Vol. II. Princeton University Press. JSTOR j.ctt1bgz9z7
Earl_A._Coddington
Logic circuit element
essentially a resonant circuit with a nonlinear reactive element which oscillates at half the driving frequency. The oscillation can be made to represent a binary
Parametron
Russian physicist and neuroscientist (1941–2025)
Mechanics Volume) of Lifshitz and Landau. The book Oscillations and Waves in Linear and Nonlinear Systems was published in 1989. Mikhail Rabinovich became
Mikhail_Rabinovich
Quantum particle
these two mesons. The solution used a phenomenon called neutral particle oscillations, by which these two kinds of mesons can turn from one into another through
Kaon
Finite difference method for numerically solving parabolic differential equations
However, the approximate solutions can still contain (decaying) spurious oscillations if the ratio of time step Δ t {\displaystyle \Delta t} times the thermal
Crank–Nicolson_method
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
Girl/Female
Tamil
Tritiya | தà¯à®°à¯€à®¤à®¿à®¯à®¾
Boy/Male
Indian
Poem
Boy/Male
Indian, Sanskrit
Having No Residence
Male
Scottish
Scottish Gaelic form of English Godfrey, GORAIDH means "God's peace."
Girl/Female
Tamil
Religious women, Courteous, Polite
Girl/Female
Arabic, Australian, French, Turkish
Lush; Flowing Water
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Tamil, Telugu
Momentary; Love; Inside Viewer
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
King of Mountains
Girl/Female
Muslim/Islamic
Daughter of Musafh; she was a narrator of hadith
Boy/Male
Indian, Mythological
One whose Fame is World Wide
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
NONLINEAR OSCILLATIONS
a.
Uniform in time; of equal time; performed in equal times; recurring at regular intervals; isochronal vibrations or oscillations.
n. pl.
Local oscillations in level observed in the case of some lakes, as Lake Geneva.