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Linear oscillators and limit-cycle oscillators qualitatively differ in terms of how they respond to fluctuations in input. In a linear oscillator, the frequency is more or less constant but the amplitude can vary greatly. In a limit-cycle oscillator, the amplitude tends to be more or less constant but the frequency can vary greatly.
The linear cable model makes several simplifications to give closed analytic results, namely that the dendritic arbor must branch in diminishing pairs in a fixed pattern and that dendrites are linear. A compartmental model [65] allows for any desired tree topology with arbitrary branches and lengths, as well as arbitrary nonlinearities. It is ...
Phase portrait of damped oscillator, with increasing damping strength. The equation of motion is x ¨ + 2 γ x ˙ + ω 2 x = 0. {\displaystyle {\ddot {x}}+2\gamma {\dot {x}}+\omega ^{2}x=0.} In mathematics , a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane .
An undamped spring–mass system is an oscillatory system. Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
The Van der Pol oscillator was originally proposed by the Dutch electrical engineer and physicist Balthasar van der Pol while he was working at Philips. [2] Van der Pol found stable oscillations, [3] which he subsequently called relaxation-oscillations [4] and are now known as a type of limit cycle, in electrical circuits employing vacuum tubes.
The artificial repressilator is a milestone of synthetic biology which shows that genetic regulatory networks can be designed and implemented to perform novel functions. However, it was found that the cells' oscillations drifted out of phase after a period of time and the artificial repressilator's activity was influenced by cell growth.
An RF oscillator produces signals in the radio frequency (RF) range of about 100 kHz to 100 GHz. [49] Oscillators designed to produce a high-power AC output from a DC supply are usually called inverters. There are two main types of electronic oscillator: the linear or harmonic oscillator and the nonlinear or relaxation oscillator. [49] [50]