ODE system phase plane

Hi guys, I have never plotted phase planes in Matlab and would like to include some graphics on a due coursework.

My ODE systems are:

dx/dt=x(r-ay)

dy/dt=c+y(bx-d)

where r,a,c,b,d are all positive constants.

I would like for the plot to include trajectories and a direction field.

Any ideas on how I could do this?

[darova]

Did you solve your equations already?

Answer 1

[Ameer Hamza]

Check my answer here to draw 2D phase plot: https://www.mathworks.com/matlabcentral/answers/519014-how-does-one-plot-phase-portraits-for-systems-of-differential-equations and here for 3D phase plot: https://www.mathworks.com/matlabcentral/answers/519154-how-do-i-plot-the-phase-space-for-a-system-of-3-odes. Also check here for more information: http://matlab.cheme.cmu.edu/2011/08/09/phase-portraits-of-a-system-of-odes/

[Martin Moreno]

This is the error I get after trying your method:

Undefined function or variable 'odeFun'.

Error in @(x,y){odeFun([],[x,y])}

[Ameer Hamza]

Martin, can you show the code which cause this error?

Answer 2

[Steven Lord]

Create an options structure using odeset. In your odeset call specify the OutputFcn option to be @odephas2, a function included with MATLAB for creating a 2-dimensional phase plane plot. Pass the options structure returned by odeset into the ODE solver as the appropriate input argument.

The orbitode example uses odephas2 in its execution.

Answer 3

[Brian Hong]

You could also use an app. I used pplane in undergrad. We also made a new app for analyzing ODE systems in the phase plane.