trying to plot a phase portrait ODE

Hi

I'm attempting to plot a phase portrait of a neuron model. The equation is;

C v' = k(v−vr)(v−vt)−u + I

u' = a{b(v−vr)−u}

if v ≥ vpeak, then

v ← c, u ← u + d

How would you go about doing this?

Answer 1

[Sally Al Khamees]

Phase Portraits are created by generating Phase Plots for different starting points. Phase plot can be created using ODEPHAS2 or ODEPHAS3 in matlab as a value for 'OUTPUTFCN' property in ODESET while creating options object. Following is an example.

function pdecaller()
    options = odeset('OutputFcn',@odephas2);
    for i=-4:4
        for j= -4:4
              [t,y] = ode45(@vdp1,[0 20],[i;j],options); hold on;
        end
    end
end

function dydt = vdp1(t,y)
     dydt = [y(2); (1-y(1)^2)*y(2)-y(1)];
end