Visualizing dynamics in Matlab

[sscnekro]

Hello, I would like to plot fixed points with corresponding basins of attraction in Matlab. I am having a system of two DE in variables $k$ and $c$ (LaTeX notation), the remaining ones are parameters:
\dot{k} = A \cdot k^{\alpha} - c - \delta \cdot k
\dot{c}= (\sigma \cdot ( A \cdot \alpha \cdot k^{\alpha - 1} - \beta - \delta)) \cdot c

I know to plot the direction field for this problem, but I would like to enhance the picture by plotting the regions. Browsing the web I found plots using ez-/contour, for a peaks based problem. I'm not having idea however, how to make contour work with my problem or if contour is actually the way to go... Hope for some of you this is an easy dab. Thanks for hints!

 

[Vailanor]

The best way to plot the fixed points and their corresponding basins of attraction is to use a Matlab function specifically designed for this purpose. The "basin" function is designed to do just that, it allows you to plot regions of attraction around any point in your system of two differential equations. The syntax for the basin function is as follows: basin(A, alpha, delta, sigma, beta, krange, crange) where A, alpha, delta, sigma, beta are the parameters of your system, krange is the range of k values to consider, and crange is the range of c values to consider. The basin function will then plot the regions of attraction and provide a color coded output of which region each point is in.