Asymptotic behaviour of solutions of Lotka–Volterra systems

New sufficient conditions for the competitive exclusion of a few species in some Lotka–Volterra systems are proved. Also an approach based on some results of the matrix Riccati equations and some ideas of the asymptotic methods is developed. In addition, conditions for the existence of finite escape times in solutions of the Lotka–Volterra systems and upper-bounds for these times are obtained.