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Empty sym: 0-by-1

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nune pratyusha
nune pratyusha on 26 Nov 2022
Edited: John D'Errico on 26 Nov 2022
clc
clear all
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syms x1 x2 x3 x4 t
tspan=[0 100];
[solx1 solx2 solx3 solx4] = solve([-x1+x2==0,-x1+x2.*x3+(0.0001+0.0001*x4.^4).*x2==0,1-x2.^2==0,x2==0], [x1, x2, x3, x4])
x1val=vpa(solx1)
x2val=vpa(solx2)
x3val=vpa(solx3)
x4val=vpa(solx4)
E1=[x1val(1,:),x2val(1,:),x3val(1,:),x4val(1,:)]
E2=[x1val(2,:),x2val(2,:),x3val(2,:),x4val(2,:)]
E3=[x1val(3,:),x2val(3,:),x3val(3,:),x4val(3,:)]
J=jacobian([-x1+x2,-x1+x2.*x3+(0.0001+0.0001*x4.^4).*x2,1-x2.^2,x2], [x1, x2, x3, x4])
J1=subs(J,{x1,x2,x3,x4},{E1(1,:)});
eigE1=round(vpa(eig(J1)),4)
J2=subs(J,{x1,x2,x3,x4},{E2(1,:)});
eigE2=round(vpa(eig(J2)),4)
J3=subs(J,{x1,x2,x3,x4},{E3(1,:)});
eigE3=round(vpa(eig(J3)),4)

Answers (1)

John D'Errico
John D'Errico on 26 Nov 2022
Edited: John D'Errico on 26 Nov 2022
Don't write a whole mess of code, withput actually thinking about whether virtially the very first (significant) line you write produces a viable result.
syms x1 x2 x3 x4 t
tspan=[0 100];
[solx1 solx2 solx3 solx4] = solve([-x1+x2==0,-x1+x2.*x3+(0.0001+0.0001*x4.^4).*x2==0,1-x2.^2==0,x2==0], [x1, x2, x3, x4])
solx1 = Empty sym: 0-by-1 solx2 = Empty sym: 0-by-1 solx3 = Empty sym: 0-by-1 solx4 = Empty sym: 0-by-1
So now look carefully at the equations you have written. I'll spread them out into 4 lines:
-x1+x2==0 (1)
-x1+x2.*x3+(0.0001+0.0001*x4.^4).*x2==0 (2)
1-x2.^2==0 (3)
x2==0 (4)
Consider the last equation. That tells you that x2 == 0.
OOPS. Look at the third equation. From that if x2==0, is there a solution? That can only happen when 1==0, and from what I recall of mathematics, that is a rare event.
Seriusly, NO! Not ever. Never. Nada. Nil. Not gonna happen.
No solution exists for this system. Now, look back at what solve told you. Empty sym. I would look far more carefully at the problem you are trying to solve. Revisit how you generated these equations.

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