Another method would be to calculate the derivative of f ( y) and evaluate it at all the fixed points. 1) If f ′ ( y) stable. 2) If f ′ ( y) > 0, the fixed point is unstable. 3) if f ′ ( y) = 0
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The equilibrium point (0, − 1) is a saddle point with global stable and unstable manifolds given by: Ws((0, − 1)) = {(x, y) | y = − 1} Wu((0, − 1)) =
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Stable And Unstable Equilibrium: Definition Potential Energy is often ignored. Students think that as long as you know Newton’s equations of
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The point x=-5.1 is an equilibrium of the differential equation, but you cannot determine its stability. You cannot determine whether or not the point x=-5.1 is an equilibrium of the
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