One of the significant results mentioned in the paper [47] concerning the functions defined on R and T 0 is as follows. Denote by C$_{rd}$ ( T $_{0}$) the set of all rd-continuous functions ϑ : T 0 → R $^{mn}$, ϑ ( t ) = { ϑ$_{ij}$ ( t ) } , and let C 1 $_{rd}$( T $_{0}$) ⊂ C$_{rd}$ ( T $_{0}$) be the set of all continuously differentiable functions on T $_{0}$, assuming that the functions have a one sided derivative at θ$_{k}$, k ∈ Z . Moreover, a function ˜ ϑ : R → R $^{mn}$, ˜ ϑ ( t ) = { ˜ ϑ$_{ij}$ ( t ) } , is an element of the set P C ( R ) if it is left-continuous on R and continuous on R \ ⋃ ∞ k = −∞ { s$_{k}$ } , and it has discontinuities of the first kind at the points s$_{k}$, k ∈ Z . The function ˜ ϑ belongs to the set P C $^{1}$( R ) if both ˜ ϑ and ˜ ϑ ′ are elements of P C ( R ) , where ˜ ϑ $^{′}$( s$_{k}$ ) = lim s → s − k ˜ ϑ ( s ) − ˜ ϑ ( s$_{k}$ ) s − s$_{k}$ , k ∈ Z . It was proved in [47] that a function ϑ ( t ) belongs to C$_{rd}$ ( T $_{0}$) ( C 1 $_{rd}$( T $_{0}$) ) if and only if ϑ ( ψ − $^{1}$( s )) belongs to P C ( R ) ( P C $^{1}$( R ) . Making use of the equation SICNN (1.2) can be written as Applying the transformation s = ψ ( t ) to (2.6) we obtain the following impulsive network, where Δ y$_{ij}$ |$_{s}$$_{=}$$_{s}$$_{k}$ = y$_{ij}$ ( s$_{k}$ +) − y$_{ij}$ ( s$_{k}$ ) and y$_{ij}$ ( s$_{k}$ +) = lim s → s + k y$_{ij}$ ( s ) , k ∈ Z . In the remaining parts of the paper, we will make use of the norm ‖ ϑ ‖ = max ( i,j ) | ϑ$_{ij}$ | , where ϑ = { ϑ$_{ij}$ } = ( ϑ$_{11}$, . . . , ϑ$_{1}$$_{n}$, . . . , ϑ$_{m}$$_{1}$ . . . , ϑ$_{mn}$ ) ∈ R $^{mn}$. The following conditions are required throughout the paper. Let us define u$_{ij}$ ( s, τ ) = e − a$_{ij}$ ( s − τ ) ∏ k ν = $_{l}$(1 − δ$_{ν}$a$_{ij}$ ) , in the case that s and τ are numbers such that s$_{l}$$_{−}$$_{1}$ < τ ≤ s$_{l}$, s$_{k}$ < s ≤ s$_{k}$$_{+1}$ for some integers k and l with k ≥ l. On the other hand, if s$_{k}$ < τ ≤ s ≤ s$_{k}$$_{+1}$ for some integer k, then take u$_{ij}$ ( s, τ ) = e − a$_{ij}$ ( s − τ $^{)}$. One can verify under the 6 (C1) δ$_{k}$a$_{ij}$ = 1 for all i = 1 , 2 , . . . , m, j = 1 , 2 , . . . , n and k ∈ Z ; (C2) λ = min ( i,j ) λ$_{ij}$ > 0 , where λ$_{ij}$ = a$_{ij}$ − 1 ψ ( ω ) p − 1 ∑ ν =0 ln | 1 − δ$_{ν}$a$_{ij}$ | ; (C3) There exists a positive number M$_{f}$ such that sup s ∈ R | f ( s ) | ≤ M$_{f}$ ; (C4) There exists a positive number L$_{f}$ such that | f ( s$_{1}$ ) − f ( s$_{2}$ ) | ≤ L$_{f}$ | s$_{1}$ − s$_{2}$ | for all s$_{1}$, s$_{2}$ ∈ R . x ′ $_{ij}$( t ) = − a$_{ij}$x$_{ij}$ ( t ) − ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij f ( x$_{hl}$ ( t )) x$_{ij}$ ( t ) + L$_{ij}$ ( t, ζ ) , t ∈ T $_{0}$, x$_{ij}$ ( θ$_{2}$$_{k}$$_{+1}$ ) = (1 − δ$_{k}$a$_{ij}$ ) x$_{ij}$ ( θ$_{2}$$_{k}$ ) − ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij f ( x$_{hl}$ ( θ$_{2}$$_{k}$ )) x$_{ij}$ ( θ$_{2}$$_{k}$ ) δ$_{k}$ + ζ ij k δ$_{k}$. (2.6) x Δ $_{ij}$( θ$_{2}$$_{k}$ ) = x$_{ij}$ ( θ$_{2}$$_{k}$$_{+1}$ ) − x$_{ij}$ ( θ$_{2}$$_{k}$ ) δ$_{k}$ , k ∈ Z , y ′ $_{ij}$( s ) = − a$_{ij}$y$_{ij}$ ( s ) − ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij f ( y$_{hl}$ ( s )) y$_{ij}$ ( s ) + L$_{ij}$ ( ψ − $^{1}$( s ) , ζ ) , s = s$_{k}$, Δ y$_{ij}$ |$_{s}$$_{=}$$_{s}$$_{k}$ = − δ$_{k}$a$_{ij}$y$_{ij}$ ( s$_{k}$ ) − ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij f ( y$_{hl}$ ( s$_{k}$ )) y$_{ij}$ ( s$_{k}$ ) δ$_{k}$ + ζ ij k δ$_{k}$, (2.7)