plotting a phase plane with a system of linear diff equations.

Hi,

I have this system of differential equations(at the very bottom), and I'm not sure how to go about plotting a phase plane. Something that looks like the graph below.(This is just an example for another set of equations.)

syms u(t) v(t)
ode1 = diff(u) == ((1/40)*v)-(u*(9/100))
ode2 = diff(v) == (u*(9/100))-(v*(9/200))   

Answer 1

[Star Strider]

Using the numeric ODE solvers, likely the easiest way to do that is to use odeset to set options, and then choose 'OutputFcn', @odephas2 as described in the documentation section on Solver Output .

syms u(t) v(t) t Y 
ode1 = diff(u) == ((1/40)*v)-(u*(9/100))

ode1(t) = 

ode2 = diff(v) == (u*(9/100))-(v*(9/200))   

ode2(t) = 

[VF,Sbs] = odeToVectorField(ode1,ode2)

VF = 

Sbs = 

ode12fcn = matlabFunction(VF, 'Vars',{t,Y})

ode12fcn = function_handle with value:
    @(t,Y)[Y(1).*(-9.0./2.0e+2)+Y(2).*(9.0./1.0e+2);Y(1)./4.0e+1-Y(2).*(9.0./1.0e+2)]

% ic = randn(2,1)
ic = [-0.4 0.2]

ic = 1×2

-0.4000 0.2000

[t,y] = ode45(ode12fcn,[0 100], ic);
for k = 1:numel(t)
    dy(:,k) = ode12fcn(t(k),y(k,:));
end

figure
plot(y(:,1), y(:,2))
grid
xlabel('y_1')
ylabel('y_2')

figure
quiver(y(:,1), y(:,2), dy(1,:).',dy(2,:).')
grid
xlabel('y_1')
ylabel('y_2')

opts = odeset('OutputFcn', @odephas2);
figure
[t,y] = ode45(ode12fcn,[0 100], ic, opts);

Error using uicontrol
This functionality is not available on remote platforms.

Error in odephas2 (line 94)
uicontrol( ...

Error in ode45 (line 269)
feval(outputFcn,[t tfinal],y(outputs),'init',outputArgs{:});

figure
plot(t, y)
grid
xlabel('t')
ylabel('y')
legend(string(Sbs))

That is the essential approach.

I will defer to you for the rest.

.

[Bryan Proa]

Thanks!

[Star Strider]

As always, my pleasure!

.