Community matrix

In mathematical biology, the community matrix is the linearization of a generalized Lotka–Volterra equation at an equilibrium point.

[1] The eigenvalues of the community matrix determine the stability of the equilibrium point.

For example, the Lotka–Volterra predator–prey model is where x(t) denotes the number of prey, y(t) the number of predators, and α, β, γ and δ are constants.

evaluated at the equilibrium point (x*, y*) is called the community matrix.

have positive real part then the equilibrium is unstable, but if all eigenvalues have negative real part then it is stable.