Equations
I have the following system of Lotka-Volterra equations:
$x'(t)=ax(t)-bx(t)y(t)$
$y'(t)=-gy(t) + dx(t)y(t)$.
This system has a non-trivial equilibrium of:
$(x^*,y^*)=(\frac{g}{d},\frac{a}{b})$.
The eigenvalues corresponding to this equilibrium are both purely imaginary:
$-i\sqrt{ag}$ and $i\sqrt{ag}$.
Question Can we conclude anything about the stability of the equilibrium (global or otherwise) despite the eigenvalues being purely imaginary?
I have been reading about the dynamics of this classic system (e.g., on Wikipedia), but have not found any information regarding the stability of the oscillatory equilibrium.
Any help would be greatly appreciated!