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English: Sadle-node singular point phase portrait with one of possible central manifolds This is a phase portrait of the simple saddle-node equation {˙ = ˙ = Its phase flow looks like: = / (/), = ()
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space.
English: Phase portrait of an undamped simple pendulum. The latest revision of the image was created in python using the source code provided below. The first revision of the image was plotted using with GNU Octave using gnuplot backend and saved as a standalone LaTeX file. The PDF generated was then converted to SVG using pdf2svg.
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Date/Time Thumbnail Dimensions User Comment; current: 19:13, 10 June 2009: 177 × 177 (30 KB): Podshumok {{Information |Description={{en|1=Phase portrait of the system with a stable focus equilibrium point}} {{ru|1=Фазовый портрет системы с особой точкой типа устойчивый фокус}} |Source=Own work by uploader
As can be seen by the animation obtained by plotting phase portraits by varying the parameter , When α {\displaystyle \alpha } is negative, there are no equilibrium points. When α = 0 {\displaystyle \alpha =0} , there is a saddle-node point.
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