Almost periodic solutions of n-species competitive system with feedback controls ✩

In this paper, the following almost periodic n-species competitive system with feedback controls ˙xi (t ) = xi (t )[bi (t )− n j=1 aij (t)xj (t )− n j=1,j =i cij (t)xi (t)xj (t )− di (t)ui (t )], ˙ui (t ) = ri (t )− ei (t)ui (t )+ fi (t)xi (t ), i = 1, 2, . . . , n, are studied by using the comparison theorem and constructing suitable Lyapunov function, where some important factors such as the effect of toxic and the age-structure are also considered simultaneously. Some sufficient conditions are obtained for the existence of a unique almost periodic solution of above model. Examples show that the obtained criteria are new, general, and easily verifiable.  2004 Elsevier Inc. All rights reserved