Everything should be stable to be observable. For example, in quantum mechanics, energy levels are those that are stable because unstable levels cannot be observed. Now, let's examine stability of 2 equilibria points in the logistic model. The difference between stable and unstable equilibria is in the slope of the line on the phase plot near the equilibrium point. The second example is the bark beetle model with two stable and two unstable equilibria.
Stable equilibria correspond to endemic and epidemic populations.
Endemic populations are regulated by the amount of susceptible trees in the forest. Epidemic populations are limited by the total number of trees because mass attack of beetle females may overcome the resistance of any tree. Stability of models with several variables Detection of stability in these models is not that simple as in one-variable models. Here, H is the density of prey, and P is the density of predators. Third, eigenvalues of matrix A should be estimated.