= Radial stability of a circular periodic orbit
{title2=$\lambda_{radial}=-r_0g\prime(r_0)$}
For $\dot r=r(a-g(r))$, $\dot\theta=1$, a positive <root of a polynomial>[root] $a=g(r_0)$ gives a <limit cycle>[circular periodic orbit] of period $2\pi$. The radial <eigenvalue>[exponent] is $-r_0g\prime(r_0)$, so $g\prime(r_0)>0$ gives <orbital stability>[orbital asymptotic stability] and $g\prime(r_0)<0$ gives <Lyapunov stability>[instability]. The phase direction is neutral; a <periodic orbit> is not an <asymptotic stability>[asymptotically stable] individual point of the flow.
Back to article page
