content_image/302872.jpg content_image/302871.jpg
auxiliary network, 

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where i, j = 1 , 2 , 3 and ζ = { ζ$_{k}$ } k ∈ Z is a solution of (6.12). The network (6.15) is the control network conjugate to (5.10). The time scale T $_{0}$, activation function f, passive decay rates a$_{ij}$ and coupling strengths C hl ij in (6.15) are the same with the ones used in (5.10). For each i and j, the external inputs L$_{ij}$ ( t, ζ ) in (6.15) are defined as L$_{ij}$ ( t, ζ ) = ζ$_{k}$ for t ∈ [ θ$_{2}$$_{k}$$_{−}$$_{1}$, θ$_{2}$$_{k}$ ] , k ∈ Z . 

Figure 2 shows the $_{z$_{22}$}$-coordinate of (6.15) corresponding to the initial data z$_{11}$ (0) = 0 . 42 , z$_{12}$ (0) = 0 . 35 , z$_{13}$ (0) = 0 . 56 , z$_{21}$ (0) = 0 . 48 , z$_{22}$ (0) = 0 . 23 , z$_{23}$ (0) = 0 . 39 , z$_{31}$ (0) = 0 . 48 , z$_{32}$ (0) = 0 . 25 , z$_{33}$ (0) = 0 . 51 and ζ$_{0}$ = 0 . 715 . The control mechanism is switched on at t = θ$_{79}$ = 139 . 5 and switched off at t = θ$_{199}$ = 349 . 5 . In the simulation, we take ε = 0 . 025 , and make use of the optimum value β$_{op}$ ≈ 0 . 4941 of the feedback gain β. It is seen in Figure 2 that the unstable 7 / 2 $_{−}$periodic solution of (5.10) is stabilized. The control becomes dominant approximately at t = 216 . 5 and its effect prolongs approximately till t = 414 , after which chaos emerges again and irregular behavior reappears. It is worth noting that the stabilization does not occur immediately after switching on the control mechanism, but rather there is a transition time. The simulation result demonstrates that it is sufficient to stabilize an unstable periodic orbit of the logistic map (5.11) to control the chaos of SICNN (5.10). 

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## 7 Conclusions 

The present study is concerned with the existence of Li-Yorke chaos in SICNNs on time scales. We rigor- ously prove the ingredients of Li-Yorke chaos, proximality and frequent separation, by taking advantage of the external inputs. This is the first time in the literature that chaos is obtained for neural networks on time scales. Our results reveal that external inputs are capable of generating chaotic outputs on time scales. The presented technique can be used to obtain chaotic SICNNs on time scales without any 

