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In electronics, a local oscillator (LO) is an electronic oscillator used with a mixer to change the frequency of a signal. This frequency conversion process, also called heterodyning, produces the sum and difference frequencies from the frequency of the local oscillator and frequency of the input signal. Processing a signal at a fixed frequency ...
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 .
A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type of information being learned.
Fessenden's receiver did not see much application because of its local oscillator's stability problem. A stable yet inexpensive local oscillator was not available until Lee de Forest invented the triode vacuum tube oscillator. [8] In a 1905 patent, Fessenden stated that the frequency stability of his local oscillator was one part per thousand. [9]
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.
A combination of quartz based reference oscillator (such as an OCXO) and modern correction algorithms can get good results in Holdover applications. [23] The holdover capability then is provided either by a free running local oscillator, or a local oscillator that is steered with software that retains knowledge of its past performance. [23]
In the bifurcation theory, a bounded oscillation that is born without loss of stability of stationary set is called a hidden oscillation.In nonlinear control theory, the birth of a hidden oscillation in a time-invariant control system with bounded states means crossing a boundary, in the domain of the parameters, where local stability of the stationary states implies global stability (see, e.g ...
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...