Consider the system of equations
where
(a) Show that the origin is the only critical point.
(b) Find the linear system that approximates Eqs. (i) near the origin and find its eigenvalues. Determine the type and stability of the critical point at the origin. How does this classification depend on
(c) Referring to Example 1 if necessary, rewrite Eqs. (i) in polar coordinates.
(d) Show that when
Note: As the parameter
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