I know that finding a Lyapunov function is not easy, so I would like to ask for any trick or hint in order to find a Lyapunov function for $$ \left\{\begin{array}{l}x'=2(x+y+z)x-7xy,\\y'=3xy-3y^2 \\ z'=2(x+y+z)z-2.2yz \\ v'=0\end{array}\right. $$ at $(0,0,0,1)$. I know that the point in asymptotically stable but would like to prove it using a Lyapunov function since the Jacobian at $(0,0,0,1)$ has all zero eigenvalues. Any help! Thanks in advance.
2026-03-27 18:08:36.1774634916
Lyapunov function for a given differential equation
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