This is the 4d Lorenz equation. how to solve it on Matlab?
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dx/dt=y+y^2-a*y*z;
dy/dt=-z^2+b*y*z-u;
dz/dt=x*y;
du/dt=-c*x;
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Yongzhen Mi
am 26 Jul. 2021
Hi, Nix Jr. I think the error is that you defined four variables in your differential equations, but you provided only three initial values to the ode45 function. Therefore, ICs should be something like this [5, 5, 5, 5]' (column vector better).
In addition, you can transfer parameters into the target function by using [time, fOUT]=ode45(@(x)test(~,x,a,b,c), t, ICs, OPTs);. In this way, the parameters a, b, and c can be claimed in the main function once, instead of being defined again and again when the target function is called.
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Yongzhen Mi
am 26 Jul. 2021
Bearbeitet: Yongzhen Mi
am 26 Jul. 2021
Take this as an example:
a = 5;
b = 20;
c = 1;
d = 0.1;
k = 0.1;
e = 20.6;
h = 1;
F = @(t,Y) [a*(Y(2)-Y(1))-e*Y(4);Y(1)*Y(3)-h*Y(2);b-Y(1)*Y(2)-c*Y(3);k*Y(2)-d*Y(4)];
CI = [3.2 8.5 3.5 2.0]';
T = linspace(0,100,3000);
[t,Y]=ode45(F,T,CI);
plot3(Y(:,1),Y(:,2),Y(:,3))
I drew some pictures and the attractors could be observed. Please try again and hopefully this will work.
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