Phase plane method

Phase plane method

In the context of nonlinear system analysis, the phase plane method refers to graphically determining the existence of limit cycles. The phase plane, applicable for second order systems only, is a plot with axes being the values of the two state variables, x_2 vs. x_1. Vectors representing the derivatives [f_2(x_1,x_2),f_1(x_1,x_2)] at representative points are drawn. With enough of these arrows in place the system behavior over the entire plane can be visualized and limit cycles can be easily identified.

External links

* [http://virtual.cvut.cz/dynlabmodules/ihtml/dynlabmodules/nonlin/node8.html Overview of the phase plane method]


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Phase plane — A phase plane is a visual display of certain characteristics of certain kinds of differential equations.Certain systems of differential equations can be written in the form::dx/dt = Cx where C may be any combination of constants in order to… …   Wikipedia

  • Phase portrait — A phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is representated by a different curve, or point.Phase portraits are an invaluable tool in studying… …   Wikipedia

  • Phase space — In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For… …   Wikipedia

  • Phase contrast microscopy — Phase contrast image of a cheek epithelial cell Phase contrast microscopy is an optical microscopy illumination technique of great importance to biologists in which small (invisible to the human eye) phase shifts in the light passing through a… …   Wikipedia

  • Methode du plan de phase — Méthode du plan de phase Demande de traduction Phase plane method → …   Wikipédia en Français

  • Méthode du plan de phase — Dans le domaine de l étude des systèmes non linéaires, la méthode du plan de phase désigne une technique qui consiste à déterminer graphiquement l existence de cycles limites. Le plan de phase, applicable uniquement aux systèmes du second ordre,… …   Wikipédia en Français

  • Method of steepest descent — For the optimization algorithm, see Gradient descent. In mathematics, the method of steepest descent or stationary phase method or saddle point method is an extension of Laplace s method for approximating an integral, where one deforms a contour… …   Wikipedia

  • Plane (Magic: The Gathering) — In Magic: The Gathering, planes are parallel universes in the Multiverse (which used to be referred to as Dominia.) Planes are often confused with planets by Magic players, because most planes are named after their primary planets. The two main… …   Wikipedia

  • Phase-shift keying — Passband modulation v · d · e Analog modulation AM · …   Wikipedia

  • Angular spectrum method — The angular spectrum method is a technique for modeling the propagation of a wave field. This technique involves expanding a complex wave field into a summation of infinite number of plane waves. Its mathematical origins lie in the field of… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”