  In a previous paper (Commun. Theor. Phys. 57 (2012) 841), we proposed a
method to distinguish poles of different dynamical origin, in a unitarized
amplitude of $\pi\pi\, K\bar K$ system. That is based on the observation that
`A Breit-Wigner resonance should exhibit two poles on different Riemann sheets
which meet each other on the real axis when $N_c=\infty$'. In this paper, we
extend our previous work (Commun.Theor.Phys. 57 (2012) 841) to the
$\pi\pi$-$K\bar K$-$\eta\eta$ three channel system. We reconfirm most of the
previous predictions. Especially the $f_0(980)$ is of $K\bar K$ molecule
nature. Other poles, including the $\sigma$, are of Breit--Wigner type.
