0 个投票

Hi , I have 2 below Eq. :
diff(V,t) = V-V.^3/3-U+2;
diff(U,t) = 1.25*(V-U+0.9);
I want to plot U'-V' plot. I don't know how to do this.
can anybidy help me please.
thanks

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Walter Roberson
Walter Roberson 2019-6-29
It appears that you will need to work numerically, as the system is difficult to solve symbolically.

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回答（1 个）

Star Strider
Star Strider 2019-6-29

0 个投票

Try this:
syms t U(t) V(t) Y
Eqs = [diff(V,t) == V-V.^3/3-U+2; diff(U,t) == 1.25*(V-U+0.9)];
[VF,Sbs] = odeToVectorField(Eqs);
UVfcn = matlabFunction(VF, 'Vars',{t,Y});
Sbsc = sprintfc('%s',Sbs);
ic = [0; 0];
tv = linspace(0, 10, 5000);
[ts,UVs] = ode45(UVfcn, tv, ic);
figure
plot(ts, UVs)
grid
figure
plot(UVs(:,1), UVs(:,2))
grid
xlabel(Sbsc(1))
ylabel(Sbsc(2))
for k = 1:numel(ts)
dUV(:,k) = UVfcn(ts(k),UVs(k,:)); % Calculate Derivatives
end
figure
plot(dUV(:,1), dUV(:,2))
grid
lblf = @(x) sprintf('$\\frac{d%s}{dt}$',x);
xlabel(lblf(Sbsc{1}), 'Interpreter','latex')
ylabel(lblf(Sbsc{2}), 'Interpreter','latex')
I will let you explore it to discover how it works.

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