In this paper, we study a system of partial differential equations describing the evolution of a population under chemotactic effects with non-local reaction terms. We consider an external application of chemoattractant in the system and study the cases of one and two populations in competition. By introducing global competitive/cooperative factors in terms of the total mass of the populations, we obtain, for a range of parameters, that any solution with positive and bounded initial data

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... es to a spatially homogeneous state with positive components. The proofs rely on the maximum principle for spatially homogeneous sub-and super-solutions. u (aoo,\u -a, 2V -ao, I u -04 J v\ and v I bo -b\u -b^v -bo, J u -b^ I v\, V Ja Ja J \ Ja Ja J respectively.