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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.
The transformation that allows this model to be solved exactly (at least in the N → ∞ limit) is as follows: . Define the "order" parameters r and ψ as = =. Here r represents the phase-coherence of the population of oscillators and ψ indicates the average phase.
In addition to graphing both equations and inequalities, it also features lists, plots, regressions, interactive variables, graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids – among other computational features commonly found in a ...
Top: Output signal as a function of time. Middle: Input signal as a function of time. Bottom: Resulting Lissajous curve when output is plotted as a function of the input. In this particular example, because the output is 90 degrees out of phase from the input, the Lissajous curve is a circle, and is rotating counterclockwise.
A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a phase space. The axes are of state variables .
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.
A function f is said to be periodic if, for some nonzero constant P, it is the case that (+) = ()for all values of x in the domain. A nonzero constant P for which this is the case is called a period of the function.
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.