I am studying the a dynamic system wherein the velocity of individuals in an area are represented by ordinary autonomous differential equations that generally looks like this: $$ m_i\left(\frac{dv_i(t)}{dt}\right)=\sum_{j(\neq i)} f_i(t) + \xi_i(t) $$
which is just the Social force model (or the acceleration formula). I am still pretty new to this but can you show me how can I find Equilibrium points and test for its stability? Resources are very unintuitive and I have to know it first in a standard model before I can apply it in a modified model.