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. The number of eigenvalues is equal to the number of state variables. In our case there will be 2 eigenvalues.
Eigenvalues are generally complex numbers.
If real parts of all eigenvalues are negative, then the equilibrium is stable. If at least one eigenvalue has a positive real part, then the equilibrium is unstable. Eigenvalues have the same meaning as the slope of a line in phase plots. Negative real parts of eigenvalues indicate a negative feedback. It is important that ALL eigenvalues have negative real parts.