(2.7) satisfy the relation It can be verified by using the last equation that where K = max ( i,j ) K$_{ij}$. Benefiting from the Gronwall-Bellman Lemma for piecewise continuous functions [77], we obtain for s ≥ s 0 that Condition ( C 6) implies that ‖ y ( s ) − φ$_{ζ}$ ( s ) ‖ → 0 as s → ∞ . Hence, ‖ x ( t ) − ϕ$_{ζ}$ ( t ) ‖ → 0 as t → ∞ , t ∈ T $_{0}$. □ The presence of Li-Yorke chaos in SICNN (1.2) will be investigated in the next section. The map (1.3) is called Li-Yorke chaotic on Λ if [27, 29]: (i) For every natural number p$_{0}$, there ex- ists a p$_{0}$ $_{−}$periodic point of F in Λ; (ii) There is an uncountable set S ⊂ Λ , the scrambled set, con- taining no periodic points, such that for every ξ$_{1}$ = { ξ ij 1 } , ξ$_{2}$ = { ξ ij 2 } ∈ S with ξ$_{1}$ = ξ$_{2}$, we have lim sup k →∞ ∥ F $^{k}$( ξ$_{1}$ ) − F k ( ξ$_{2}$ ) ∥ > 0 and lim inf k →∞ ∥ F $^{k}$( ξ$_{1}$ ) − F $^{k}$( ξ$_{2}$ ) ∥ = 0; (iii) For every ξ$_{1}$ ∈ S and a periodic point ξ$_{2}$ ∈ Λ , we have lim sup k →∞ ∥ F $^{k}$( ξ$_{1}$ ) − F $^{k}$( ξ$_{2}$ ) ∥ > 0 . Denote by Θ the set of all sequences ζ = { ζ$_{k}$ }$_{k}$$_{∈}$$_{Z}$ obtained by equation (1.3). We say that a pair of sequences ζ = { ζ$_{k}$ }$_{k}$$_{∈}$$_{Z}$ , ˜ ζ = { ˜ ζ$_{k}$ } k ∈ Z ∈ Θ is proximal if lim inf k →∞ ∥ ζ$_{k}$ − ˜ ζ$_{k}$ ∥ = 0 , and it is frequently separated if lim sup k →∞ ∥ ζ$_{k}$ − ˜ ζ$_{k}$ ∥ > 0 . →∞ Let A be the collection of all bounded solutions ϕ$_{ζ}$ ( t ) = { ϕ ij ζ ( t ) } of (1.2) such that ζ ∈ Θ . A pair ϕ$_{ζ}$ ( t ) , ϕ$_{˜}$ $_{ζ}$( t ) ∈ A is proximal if for an arbitrary small positive number ϵ and an arbitrary large natural number E, there exists an integer k$_{0}$ such that ∥ ϕ$_{ζ}$ ( t ) − ϕ$_{˜}$ $_{ζ}$( t ) ∥ < ϵ for all t ∈ [ θ$_{2}$$_{k}$$_{0}$$_{−}$$_{1}$, θ$_{2(}$$_{k}$$_{0}$$_{+}$$_{E}$$_{)}$ ] ∩ T $_{0}$. On the other hand, the pair ϕ$_{ζ}$ ( t ) , ϕ$_{˜}$ $_{ζ}$( t ) ∈ A is frequently ( ϵ$_{0}$, ϵ$_{1}$ $_{)}$-separated if there exist numbers ϵ$_{0}$ > 0 , ϵ$_{1}$ > 0 and infinitely many disjoint intervals J$_{q}$ ⊂ T $_{0}$, q ∈ N , each with a length no less than ϵ$_{1}$ such that 9 4 Li-Yorke chaos ‖ y ( s ) − φ$_{ζ}$ ( s ) ‖ ≤ K (1 + δd ) p ∥ x$_{0}$ − φ$_{ζ}$ ( s $^{0}$) ∥ e [ − λ + d + p ln(1+ δd ) /ψ ( ω $^{)]}$( s − s $^{0}$) . ‖ y ( s ) − φ$_{ζ}$ ( s ) ‖ ≤ Ke − λ ( s − s $^{0}$) ∥ x$_{0}$ − φ$_{ζ}$ ( s $^{0}$) ∥ + ∫ s s 0 de − λ ( s − τ ) ‖ y ( τ ) − φ$_{ζ}$ ( τ ) ‖ dτ + ∑ s $^{0}$≤ s$_{k}$<s δde − λ ( s − s$_{k}$ ) ‖ y ( s$_{k}$ ) − φ$_{ζ}$ ( s$_{k}$ ) ‖ , y$_{ij}$ ( s ) − φ ij ζ ( s ) = u$_{ij}$ ( s, s $^{0}$) ( x ij 0 − φ ij ζ ( s $^{0}$) ) − ∫ s s 0 u$_{ij}$ ( s, τ ) ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij [ f ( y$_{hl}$ ( τ )) y$_{ij}$ ( τ ) − f ( φ hl ζ ( τ )) φ ij ζ ( τ ) ] dτ − ∑ s $^{0}$≤ s$_{k}$<s u$_{ij}$ ( s, s$_{k}$ +) ∑ C$_{hl}$ ∈ N$_{r}$ ( i,j ) C hl ij [ f ( y$_{hl}$ ( s$_{k}$ )) y$_{ij}$ ( s$_{k}$ ) − f ( φ hl ζ ( s$_{k}$ )) φ ij ζ ( s$_{k}$ ) ] δ$_{k}$.