Permanence of ecological systems

Given a mathematical model of an ecological/biological community, can one find out whether the whole community will survive? Is there is a global attractor in which all species/types of the system coexist? If the state space is the nonnegative orthant ${\mathbb R}^n_+$ this means that its boundary (together with $\infty$) is a repeller for the dynamics.

I will describe some methods and results about this problem.

Important tools are Lyapunov exponents and average Lyapunov functions.