Concept of scientific equilibrium: chemical equilibrium, ecological equilibrium, thermodynamic equilibrium. etc. These scientific concepts of equilibrium are modeled by the mathematical notion of an equilibrium point of a vector field.
definition of stable and unstable EP
ball in a bowl, ball on a hill
semi-stable equilibrium points
EPs in 1D: start with simple class: linear.
EPS of \( X' = kX \) and \( X' = -kX \)