I was wondering whether there exists an ODE system that has a global attractor that cannot be established using a Lyapunov function. That is, is it true that the existence of a Lyapunov function is not a necessary condition for global attraction in general? And what is the situation if we replace global with local in the aforementioned sentences?
2026-03-27 23:57:25.1774655845
Is there an attractor that cannot be established using a Lyapunov function?
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