So far, we have the concepts of state space, model, vector field, trajectory, Euler’s method.
With these concepts we can calculate the behavior predicted by any model. Is that all there is? do we just generate models and then simulate the models to get their behavior?
No, there are also powerful mathematical techniques that can give us a big picture of how a system will behave, so that we can get the "lay of the land" in state space
An example in 1D: The logistic model \( X' = bX(1-\dfrac{X}{k}) \) the vector field has to have an \( X' = 0 \) in the middle find it as \(X = k \) by solving \( X' = 0 \)
Definition of an Equilibrium Point
finding EPs in logistic and Allee models