Say we have a non-linear system. The system has an equilibrium point at $0$. Say that we linearize the system around the equilibrium point. The transformed linear system comes up to be unstable. From that we can conclude that the equilibrium point at the initial (non-linear) system is also locally unstable. Does being locally unstable mean that the equilibrium point is also globally unstable?
2026-03-28 06:23:31.1774679011
Conclusion for global stability according to local stability
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