How to determine the direction a stable focus (source) or unstable focus (sink) is rotating, given the eigenvalues $\lambda=\alpha\pm\beta i$ ?
I know that if $\alpha > 0$ then it is source and if $\alpha < 0$, then it is a sink. This poses no problem.
However, for instance, in the book Dynamical Systems with Applications using Maple (S. Lynch), p.38 is stated that $\dot \theta = -\beta$ and if $\dot \theta > 0$, then the spiral is rotating counter-clockwise and if $\dot \theta < 0$, then the spiral is rotating clockwise. The problem is the $\pm$ sign - there are two $\beta$s - one positive and one negative. How to determine the direction of the spiral motion?