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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.
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.
The entire field is the phase portrait, a particular path taken along a flow line (i.e. a path always tangent to the vectors) is a phase path. The flows in the vector field indicate the time-evolution of the system the differential equation describes.
The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas. The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and ...
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.
The same plot as a 3D diagram. ... The red dots in the phase portraits are at times which are an integer multiple of the period = /. [11] ...
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: = / (/), = ()
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.