Empty sym: 0-by-1

clc

clear all

close all

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)

Answer 1

[John D'Errico]

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.