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∥ ϕ$_{ζ}$ ( t ) − ϕ$_{˜}$ $_{ζ}$( t ) ∥ > ϵ$_{0}$ for each t from these intervals. Moreover, ϕ$_{ζ}$ ( t $_{)}$, ϕ$_{˜}$ $_{ζ}$( t ) ∈ A is a Li-Yorke pair if it is proximal and frequently ( ϵ$_{0}$, ϵ$_{1}$ $_{)}$-separated for some positive numbers ϵ$_{0}$ and ϵ$_{1}$. 

The SICNN (1.2) is called Li-Yorke chaotic if: (i) There exists a p$_{0}$ω $_{−}$periodic solution of (1.2) for each p$_{0}$ ∈ N ; (ii) There exists an uncountable set Σ ⊂ A , the scrambled set, which does not contain any periodic solution, such that any pair of different solutions of (1.2) inside Σ is a Li-Yorke pair; (iii) For any ϕ$_{ζ}$ ( t ) ∈ Σ and any periodic solution ϕ$_{˜}$ $_{ζ}$( t ) ∈ A , the pair ϕ$_{ζ}$ ( t $_{)}$, ϕ$_{˜}$ $_{ζ}$( t ) is frequently ( ϵ$_{0}$, ϵ$_{1}$ $_{)}$-separated for some positive numbers ϵ$_{0}$ and ϵ$_{1}$. 

One can confirm that the sequence { η$_{k}$ } is p $_{−}$periodic, where η$_{k}$ = θ$_{2}$$_{k}$ − θ$_{2}$$_{k}$$_{−}$$_{1}$, k ∈ Z . Suppose that η = min 1 ≤ k ≤ p η$_{k}$ and η = max 1 ≤ k ≤ p η$_{k}$. We will denote by i ( J ) the number of the terms of the sequence { s$_{k}$ }$_{k}$$_{∈}$$_{Z}$ that belong to the interval J ⊂ R . It can be verified that i ([ a$_{0}$, b$_{0}$ )) ≤ p + p ψ ( ω ) ( b$_{0}$ − a$_{0}$ ) for any real numbers a$_{0}$, b$_{0}$ such that b$_{0}$ > a$_{0}$. 

The proximality feature of bounded solutions of SICNN (1.2) will be mentioned in the following lemma. 

Lemma 4.1 Assume that the conditions ( C 1) − ( C 6) are satisfied. If a pair of sequences ζ, ˜ ζ ∈ Θ is proximal, then the same is true for the pair ϕ$_{ζ}$ ( t ) , ϕ$_{˜}$ $_{ζ}$( t ) ∈ A . 

Proof. Throughout the proof, let us denote 

and 

Assume that γ is a real number which satisfies the inequality 

<img src='content_image/296526.jpg'>

<img src='content_image/296525.jpg'>

<img src='content_image/296524.jpg'>

Fix an arbitrary small number ϵ > 0 and an arbitrary large natural number E such that 

Since the pair ζ, ˜ ζ is proximal, there exists an integer k$_{1}$ such that 

<img src='content_image/296523.jpg'>

<img src='content_image/296522.jpg'>

