The complete classification of asymptotic behavior for bounded cooperative Lotka-Volterra systems with the assumption (SM)

Abstract

Assume that the n n -dimensional Lotka-Volterra system is cooperative with the assumption ( S M ) : a i i > 0 , a i j > 0 \left ( SM \right ) : {a_{ii}} > 0, {a_{ij}} > 0 for all i ≠ j i \ne j , and all solutions of the system are bounded. Then we give a complete classification of the behavior of the solutions. This classification does not require any restriction on the auto-increase coefficients.