The next section is devoted to the existence as well as the exponential stability of almost periodic solutions of (2.3). Let us denote by B$_{0}$ ( R ) the set of all bounded and continuous functions defined on R . For g ∈ B$_{0}$ ( R ) and α ∈ R , a translation of g by α is a function Q$_{α}$g ( t ) = g ( t + α ) , t ∈ R . A number α ∈ R is called an ϵ − translation number of a function g ∈ B$_{0}$ ( R ) if || Q$_{α}$g ( t ) − g ( t ) || < ϵ for every t ∈ R . Besides, a set S ⊂ R is said to be relatively dense if there exists a number h > 0 such that [ ϑ, ϑ + h ] ∩ S =  for all ϑ ∈ R . A function g ∈ B$_{0}$ ( R ) is said to be almost periodic, if for every positive number ϵ, there exists a relatively dense set of ϵ − translation numbers of g [76]. On the other hand, an integer k$_{0}$ is called an ϵ − almost period of a sequence { a$_{p}$ } , p ∈ Z , of real numbers if | a$_{p}$$_{+}$$_{k}$$_{0}$ − a$_{p}$ | < ϵ for any p ∈ Z [77]. Let ζ q p = ζ$_{p}$$_{+}$$_{q}$ − ζ$_{p}$ and θ q p = θ$_{p}$$_{+}$$_{q}$ − θ$_{p}$ for all p and q. We call the family of sequences { ζ q p } , q ∈ Z , equipotentially almost periodic [22, 77, 78] if for an arbitrary positive number ϵ there exists a relatively dense set of ϵ − almost periods, common for all sequences { ζ q p } , q ∈ Z . The following conditions are required. 5 Almost periodic solutions 13 The existence and exponential stability of the almost periodic solution of the network (2.3) is men- tioned in the following theorem. It follows from condition ( C 8) that there exists a positive number ¯ θ such that condition ( C 3) is valid, and | θ$_{p}$ | , | ζ$_{p}$ | → ∞ as | p | → ∞ [22, 77, 78]. The next assertion can be proved by the method of common almost periods developed in [79] (see also [77, 78]). Lemma 5.1 [78] Assume that L ( t ) = { L$_{ij}$ ( t ) } , i = 1 , 2 , . . . , m, j = 1 , 2 , . . . , n is almost periodic and the conditions ( C 8) , ( C 9) are valid. Then, for arbitrary η > 0 , 0 < ν < η, there exist relatively dense sets of real numbers Ω and integers Q such that (i) ‖ L ( t + α ) − L ( t ) ‖ < η, t ∈ R ; (ii) | ζ q p − α | < ν, p ∈ Z ; (iii) | θ q p − α | < ν, p ∈ Z , α ∈ Ω , q ∈ Q. (C8) The sequences { ζ q p } , q ∈ Z , as well as the sequences { θ q p } , q ∈ Z , are equipotentially almost periodic; (C9) There exist positive numbers θ and ζ such that θ$_{p}$$_{+1}$ − θ$_{p}$ ≥ θ and ζ$_{p}$$_{+1}$ − ζ$_{p}$ ≥ ζ for all p ∈ Z .