2.2: Equilibrium Solutions and Stability

From this it is clear (hopefully) that \(y = 2\) is an unstable equilibrium solution and \(y = -2\) is an asymptotically stable equilibrium solution. However, \(y = -1\) behaves differently from either of these two.

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What is an equilibrium solution to a differential equation?

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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The term ‘equilibrium’ is derived from two Latin words called “acqui” and “libra”. “Acqui” means equal and “libra” refers to balance. Hence, equilibrium means ‘equal balance’. The term ‘equilibrium’ is substantially used
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Differential Equations Equilibria and Stability

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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