The equilibrium points of the logistic differential equation are like linear EPS
the equilibrium points of all differential equations are like linear EPs. Principle of Linearization (Hartman-Grobman Theorem)
A way of finding stability: make a vector-field plot of \( X' \) against \( X \), and look at the slope of the points where the function crosses \( X' = 0 \).
1D: look at \( \dfrac{dX'}{dX} \)
graphing the function \( X' = f(X) \) case of logistic
Calculation of Linear Stability Analysis for logistic and Allee, both algebraically and geometrically.