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The nonlinear system is: $\dot{x}_1=\frac{5}{2}-2x_2-\frac{3}{2}x_1+x_2x_1$ and $\dot{x}_2=x_1-\frac{5}{2}$.

My problem is trying to find the Lyapunov function for this system, if one exists. I've been using the Sums of Squares Method, but it doesn't work for this system. Even MatLab's been throwing up errors when I tried using SOSTools. Any ideas?

Desperate Fluffy
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  • I don't think there is one because there is only one equilibrium point which is a saddle point. – KittyL Jun 18 '15 at 16:42
  • How did you determine that? – Desperate Fluffy Jun 18 '15 at 16:45
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    Solve $x_1-\frac{5}{2}=0$ and $\frac{5}{2}-2x_2-\frac{3}{2}x_1+x_2x_1=0$. Then find the Jacobian matrix and plug these numbers in. The eigenvalues of the matrix are two real numbers having different signs. That means it is a saddle. – KittyL Jun 18 '15 at 17:08

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