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Just wondering how you're supposed to classify an equilibrium point if one of the eigenvalues is zero and the other is a negative real number. The linearisation theorem fails here and I don't know how to classify the point otherwise.

The only other information I've got is that there is a vertical isocline through the equilibrium point. The isocline is always positive in direction and does not change sign when it intersects the point.

Any help would be greatly appreciated

Anon
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  • I suppose it will depend of the system as the stability of the ODE version. If you provide us more information about the system we may help you with the way to do it. – energy May 19 '20 at 10:49
  • Just realised that the other eigenvalue is negative if that changes anything. Is there any way to know what it could be? All of the types of equilibrium points I'm aware of (node, saddle, spiral, centre, star, degenerate node) fail here. Are there more types of equilibrium point that I'm unaware of? – Anon May 19 '20 at 11:05
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    Indeed, it changes everything (the other case, with at least one positive eigenvalue, is trivial). In this case, without the actual system it is impossible to say more. – John B May 19 '20 at 13:40

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