12 questions linked to/from Basins of Attraction
750 views

Plot basins of attraction using separatrices for particular pendulum [duplicate]

How can I plot the stable and unstable separatrices to make a graphic of the basins of attraction of this differential equation? ...
270 views

Plotting basin boundary [duplicate]

How to plot the basin boundary in Mathematica? I have been trying to do this using the system ...
2k views

Phase portrait on a cylinder

It is very nice and very easy to make a sketch of a phase portrait with StreamPlot. For example, for the classical pendulum, defined by \begin{eqnarray*} \dot x&...
3k views

Plotting separatrices for nonlinear system

Consider the system: \begin{align*} x'&=(1-x-y)x\\ y'&=(4-7x-3y)y \end{align*} The system has a saddle point at (1/4,3/4). How can I plot the separatrices on the phase portrait having domain ...
737 views

How to draw the image of a circle under the action of a transformation of the phase flow?

How to draw the image of a circle $x^2+(y-1)^2<1/4$ under the action of a transformation of the phase flow for the equation $\dot{x}=y,\ \dot{y}=-\sin x$? Here $\dot{x}$ means $dx/dt$. Any help or ...
2k views

Getting clearer StreamPlot output

When I do a StreamPlotof a rather complicated pair of differential equations, it loses some details. For example: ...
424 views

How to plot GDPs in this way?

Actually the current answer is very wonderfull.The bouns just for someone can complete this question. I found this interesting plot of how the relationship between the GDPs of different countries has ...
361 views

Finding the attractors of the vector field constructed as the gradient of an interpolated 3D scalar field

I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar ...
536 views

Phase Portrait Trajectories

How do I make a phase portrait which looks like the ones demonnstrated here? Not the fancy version where I can use the controls to change it, just a screen-shotted version of say a spiral point? Any ...
305 views

Plotting Invariant Manifolds of the Henon Map

Given the following map: \begin{align} & x_{n+1}=-y_n+2x_n^2 \\ & y_{n+1}=\beta x_n \end{align} for $β \in (0,1)$, $x_n \in \mathbb{R}, y_n \in \mathbb{R}$ (which is a one parameter version ...