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Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence. In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point.
In addition, an oscillating system may be subject to some external force, as when an AC circuit is connected to an outside power source. In this case the oscillation is said to be driven . The simplest example of this is a spring-mass system with a sinusoidal driving force.
The differential equation is called oscillating if it has ... "Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function". ...
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency.
The model is derived by modeling an electron orbiting a massive, stationary nucleus as a spring-mass-damper system. [2] [3] [4] The electron is modeled to be connected to the nucleus via a hypothetical spring and its motion is damped by via a hypothetical damper. The damping force ensures that the oscillator's response is finite at its ...
The Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀, Kuramoto Yoshiki), [1] [2] is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators .
The function Φ(t,x) is called the evolution function of the dynamical system: it associates to every point x in the set X a unique image, depending on the variable t, called the evolution parameter. X is called phase space or state space , while the variable x represents an initial state of the system.
The Weierstrass approximation theorem states that for every continuous function f(x) defined on an interval [a,b], there exists a set of polynomial functions P n (x) for n=0, 1, 2, ..., each of degree at most n, that approximates f(x) with uniform convergence over [a,b] as n tends to infinity, that is,