I'm working on a linear stability analysis and have reached a quadratic that led me to two eigenvalues of opposite signs. $$\chi s^2 + \bigg [\frac{\chi v^\infty}{d_c} - \frac{\chi\beta}{\zeta} - k + \frac{\tau_c (A_0-A_f^{ss})}{d_c} \bigg ]s + \frac{\beta k}{\zeta}- \frac{k v^\infty}{d_c}$$
Plugging in all the variables led me to two eigenvalues of s $\approx $ 0.0321 and $s\approx -0.001222$
What can I conclude from this? What other analysis can be done to find more information about the stability of my system - Does this saddle point mean it is unstable? I have been changing k as a part of my analysis and get different values but always one positive and one negative.