Stability of Degenerate Critical Points: A Phase Plane Analysis

dirk_mec1
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How can you determine the stability of a critical point which is degenerate?
 
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Phase plane analysis. You could have periodic solutions. It helps to know if your problem is a perturbation of a linear system (Th. of ODE: Coddington, Levinson).
 
gammamcc said:
Phase plane analysis. You could have periodic solutions. It helps to know if your problem is a perturbation of a linear system (Th. of ODE: Coddington, Levinson).

So I should always grab Maple and stare at the ( immediate environment of the) equibrilium point?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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