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Differential Equations

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Cubic Nonlinearity: The Stability of the Critical Point

DIFFEQ-I3HFY6

Consider the nonlinear system

$\dot{x}=-x^3-y^3$,
$ \dot{y}=2xy^2$.

This system is not locally linear and the nonlinearity is cubic. What is the stability of the critical point $(0,0)$?

A

Unstable

B

Stable but not asymptotically stable

C

Asymptotically stable

D

The stability can't be determined