paper are true or can be easily adapted to the following systems, that is, differential equations with piecewise constant argument, EP CAG, differential equations with variable delay and piecewise constant argument, In other words, what we have suggested are sufficiently general models, which can be easily specified for concrete applications. Let us introduce the initial condition for SICNN (2.3). Fix a number σ ∈ R and functions φ = { φ$_{ij}$ } , ψ = { ψ$_{ij}$ } ∈ C , i = 1 , 2 , . . . , m, j = 1 , 2 , . . . , n. In the case γ ( σ ) < σ, we say that a solution x ( t ) = { x$_{ij}$ ( t ) } of (2.3) satisfies the initial condition and write x ( t ) = x ( t, σ, φ, ψ ) , t ≥ σ, if x$_{σ}$ ( s ) = φ ( s ) , x$_{γ}$$_{(}$$_{σ}$$_{)}$ ( s ) = ψ ( s ) for s ∈ [ − τ, 0] . In what follows, we assume that if the set [ γ ( σ ) − τ, γ ( σ )] ∪ [ σ − τ, σ ] is connected, then the equation φ ( s ) = ψ ( s + σ − γ ( σ )) is true for all s ∈ [ − τ, γ ( σ ) − σ ] . If γ ( σ ) ≥ σ, then we look for a solution x ( t ) = x ( t, σ, φ ) , t ≥ σ, such that x$_{σ}$ ( s ) = φ ( s ) , s ∈ [ − τ, 0] . Thus, if θ$_{p}$ ≤ σ < θ$_{p}$$_{+1}$ for some p ∈ Z , then there are two cases of the initial condition: (IC$_{1}$) x$_{σ}$ ( s ) = φ ( s ) , φ ∈ C , s ∈ [ − τ, 0] if θ$_{p}$ ≤ σ ≤ ζ$_{p}$ < θ$_{p}$$_{+1}$ ; (IC$_{2}$) x$_{σ}$ ( s ) = φ ( s ) , x$_{γ}$$_{(}$$_{σ}$$_{)}$ ( s ) = ψ ( s ) , φ, ψ ∈ C , s ∈ [ − τ, 0] , if θ$_{p}$ ≤ ζ$_{p}$ < σ < θ$_{p}$$_{+1}$. Considering SICNN (2.3) with these conditions, we shall say about the initial value problem ( IV P ) for (2.3). To be short, we shall say only about IV P in the form x ( t, σ, φ, ψ ) , specifying x ( t, σ, φ ) for ( IC$_{1}$ ) , if needed. Thus, we can provide the following definitions now. Definition 2.1 A function x ( t ) = { x$_{ij}$ ( t ) } , i = 1 , 2 , . . . , m, j = 1 , 2 , . . . , n, is a solution of (2.3) with ( IC$_{1}$ ) or ( IC$_{2}$ ) on an interval [ σ, σ + a ) if: (i) it satisfies the initial condition; (ii) x ( t ) is continuous on [ σ, σ + a ); (iii) the derivative x $^{′}$( t ) exists for t ≥ σ with the possible exception of the points θ$_{p}$ , where one-sided derivatives exist; 6 dx$_{ij}$ dt = − a$_{ij}$x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) C kl ij f ( x$_{kl}$ ( γ ( t ))) x$_{ij}$ + L$_{ij}$ ( t ) , (2.4) dx$_{ij}$ dt = − a$_{ij}$x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) C kl ij f ( x$_{kl}$ ( t − τ ( t )) , x$_{kl}$ ( γ ( t ) − τ ( t ))) x$_{ij}$ + L$_{ij}$ ( t ) , (2.5) dx$_{ij}$ dt = − a$_{ij}$x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) C kl ij f ( x$_{kl}$ ( t − τ ( t ))) x$_{ij}$ − ∑ C$_{kl}$ ∈ N$_{r}$ ( i,j ) D kl $_{ij}$g ( x$_{kl}$ ( γ ( t ))) x$_{ij}$ + L$_{ij}$ ( t ) . (2.6)